ENVIRONMENTAL 
DESIGN 
LIBRARY 


GIFT  OF 


John  Staley 


MECHANICAL    DRAWING 

TECHNIQUE    AND    WORKING    METHODS 


FOR   TECHNICAL   STUDENTS 


BY 

CHARLES    L.   ADAMS 

PROFESSOR   OF   DRAWING   AND   DESCRIPTIVE   GEOMETRY    IN   THE 
MASSACHUSETTS    INSTITUTE    OF   TECHNOLOGY 


SIXTH  EDITION 
REVISED 


BOSTON 

PRESS    OF   GEO.  H.  ELLIS   CO. 
1913 


DESIGH  LIBRARY 


COPYRIGHT,   IQOS,  BY  CHARLES  L.  ADAMS 


PREFACE. 

A  thorough  preparation  in  drawing  for  a  course  in  engineering  or  in  archi- 
tecture should  include  the  study  of  descriptive  geometry  or  the  principles  of  rep- 
resentation ;  the  training  of  the  sense  powers  to  give  precision  and  facility 
in  the  technique  of  drawing ;  and  instruction  in  practical  freehand  drawing.  This 
book,  treating  of  the  second  of  the  requirements  named  and  of  technical  methods 
in  execution,  has  been  prepared  for  use  in  the  first-year  courses  in  drawing  and 
descriptive  geometry  at  the  Massachusetts  Institute  of  Technology.  It  is  not 
intended  as  a  prescribed  set  of  exercises  to  be  taken  in  the  same  form  by  all  stu- 
dents, but  rather  as  a  collection  of  material  sufficient  to  enable  the  teacher,  by 
judicious  selection,  to  lay  out  the  work  of  a  course,  whether  designed  solely  for 
educational  training,  or  as  an  introduction  to  a  particular  course  in  engineering  or 
architecture,  or  for  a  further  specialization  to  meet  the  need  of  individual  students. 

To  make  up  as  far  as  possible  for  the  inevitable  loss,  in  large  classes,  of  indi- 
vidual instruction  in  details  —  so  necessary  for  the  best  results  in  technique  —  a 
large  number  of  explanatory  cuts  has  been  introduced  and  minor  processes  have 
been  fully  explained.  This  detailed  presentation,  together  with  the  subjects  con- 
sidered briefly  in  the  last  chapter,  should,  it  is  believed,  make  the  book  useful  for 
reference  in  the  student's  future  professional  work. 

The  subject  of  projection,  usually  presented  in  text-books  on  mechanical 
drawing  has  been  here  omitted  in  the  belief  that,  when  a  course  includes  descrip- 
tive geometry,  it  is  unnecessary  to  give  a  portion  of  this  subject  under  a  different 
name.  Furthermore,  drawing  from  actual  objects  appears  to  be  the  best  educa- 
tional and  practical  introduction  to  descriptive  geometry. 

Special  care  has  been  given  to  the  originals  for  the  plates,  which  were  drawn 
strictly  in  accordance  with  the  directions  in  the  practice  exercises.  The  author 
desires  to  express  his  thanks  to  Mr.  H.  C.  Bradley  and  Mr.  A.  T.  Robinson  for 
much  valuable  help  with  the  text,  and  to  other  members  of  the  Institute  instruct- 
ing staff  for  suggestions  and  criticism. 


CONTENTS. 


CHAPTER  PAGE 

I.     DRAWING  INSTRUMENTS  AND  MATERIALS  ;  THEIR  SELECTION i 

II.     USES  AND  CARE  OF  THE  INSTRUMENTS  AND  MATERIALS;    MANIPULATION.  14 

III.  RENDERING;    CONVENTIONS;    LETTERING    AND    DIMENSIONING;    COMMON 

WORKING  METHODS 36 

IV.  STUDY  PLATES  ON  INSTRUMENTAL  RENDERING  AND  CONSTRUCTION      .     .  59 
V.     GEOMETRICAL  CONSTRUCTION , 79 

VI.     SELECTION  AND  ARRANGEMENT 102 

VII.     OBJECT  DRAWING 109 

VIII.     WORKING  DRAWINGS 143 

IX.     PSEUDO-PICTORIAL  REPRESENTATION;  ISOMETRIC  DRAWING 155 

X.     WASH  DRAWING 166 

XI.     MECHANICAL   COPYING;   THE  BLUE-PRINT   PROCESS;    PROCESS   DRAWING; 

PATENT  OFFICE  DRAWING 183 


MECHANICAL    DRAWING 


CHAPTER   I. 

DRAWING  INSTRUMENTS   AND   MATERIALS  —  THEIR  SELECTION. 

1.  Mechanical  Drawing  —  the  language  of  engineering,  architecture,  and  the 
mechanic  arts  —  is  representation  based  on  descriptive  geometry  and  expressed 
by  means  of  drawing  instruments.     In  the  representation  of  objects,  mechanical 
drawing  deals  primarily  with  actual  figure  and  measurement,  and  is  not  in  general 
concerned  with  the  appearance  of  things. 

2.  The  Instruments  usually  required  for  outline  drawing  are  illustrated  in 
Plates   i   and   2.     Several  special  instruments  and  materials  for  brush  work  are 
shown  in  Plate  3.     The  following  list  represents  the  complete  equipment  for  the 
drawing  exercises  here  given.     In  procuring  the  instruments,  it  is  advisable  for 
the  beginner  to  intrust  their  selection  to  an  experienced  draftsman ;  but,  if  this 
is  impracticable,  he  should  read  Articles  3-13  before  purchasing. 

1  Set  of  Instruments. 

2  Drawing  Boards,  1 1^  x  I5|  in.  and  17  x  22!  in. 
2  T-squares,  1 5-inch  and  21 -inch,  fixed  head. 
Rubber  or  Amber  Triangles  as  follows  :  — 

i  45°-45°,    4-inch. 

i  45°-45°,    8    « 

i  30°-6o°,    5    " 

i  30°-6o°,  10    " 

2  Irregular  Curves  (of  the  shapes  shown  in  Plate  2). 
i  12-inch   Architect's  Triangular  Scale  (divided  into  sixteenths   of   an  inch 

and  scales  cf  ^,  T3g,  J,  J,  f,  J,  f,  i,  i J,  and  3  in.  to  a  foot), 
i  Pricker. 


DRAWING  INSTRUMENTS  AND  MATERIALS  —  THEIR  SELECTION. 

Drawing  Papers  (in  a  strong  envelope,  17  x  22^  in.),  as  follows  :  — 

3  Sheets  Whatman's  Half  Imperial,  cold  pressed. 

6       "  "  "  "          hot         " 

6       "      Duplex  Detail  Paper  (cut  half  imperial  size). 

6       "      Tracing  Cloth  (cut  half  imperial  size). 

2       "      Rowney's  Roll  Tracing  Paper  (cut  half  imperial  size). 
i  Block  of  White  Practice  Drawing  Paper,  1 1  x  15  in.,  24  sheets. 
i  Dozen  Thumb  Tacks. 
3  "Koh-i-noor"  Pencils,  H,  4.H,  and  6H. 
i  6H  "Koh-i-noor"  Lead  (for  the  compasses). 
i  Fine  File,  or  Sandpaper  Pad  (for  sharpening  pencils), 
i  Stick  India  Ink,  super-super,  half  size, 
i  Slate  Ink  Slab,  with  cover, 
i  Emerald  Rubber, 
i  Sand  Rubber,  T3g  x  i  x  i|  in. 
i  Steel  Eraser. 

i  Agate  Burnisher  (of  the  form  shown  in  Plate  2). 
i  Piece  Chamois  Skin,  size  about  lox  12  in. 
i  Fine  Oil  Stone,  3-inch  (for  sharpening  ruling  pens). 

1  Penholder  and  Pens,  —  \  doz.  each  of  Gillott's  303,  and  D.  Leonard  &  Co.'s 
Ball  Point,  521  F. 

2  Camel-hair  Brushes  (of  the  sizes  shown  in  Plate  3). 

i  Water  Glass  and  Tumbler  (of  the  size  given  in  Plate  3). 

i  Medium  Sized  Sponge. 

i  3-oz.  Jar  Drawing  Board  Paste. 

i  Sketch  Book,  7x8^  in.,  ledger  paper,  100  pages. 

i  6-inch  Calipers. 

i  2-foot  Folding  Rule. 


DRAWING  INSTRUMENTS  AND  MATERIALS  —  THEIR  SELECTION.         3 

3.  The  Set  of  Instruments  (Fig.  i).  The  essential  characteristic  of  a  good 
instrument  is  that,  when  put  in  satisfactory  working  order,  it  remains  so  for  a 
reasonable  length  of  time, —  a  condition  dependent  upon  excellence  of  material  and 


Fig.  i. 

of  workmanship  in  making  the  joints  and  tempering  the  points  of  the  instrument. 
The  difference  between  a  good  and  an  inferior  instrument  may  not  be  easily  recog- 
nized through  inspection  alone,  as  the  appearance  of  the  better  grades  is  extensively 


DRAWING  INSTRUMENTS  AND  MATERIALS  —  THEIR  SELECTION. 


imitated.  To  the  beginner  a  set  at  three  dollars  may  appear  quite  as  good  as  one 
at  twenty  dollars.  Hence  his  guide  must  be  the  selling  price  by  a  reputable  dealer, 
which  is  from  eight  to  twenty-eight  dollars  a  set  according  to  quality.  For  the 
best  results  in  drawing,  and  for  wear,  the  best  instruments  are  necessary.  A  very 
good  set,  but  not  the  best,  includes  :  the  best  imitation  of  the  Alteneder  pivot- 
joint*  compass ;  Alteneder-style  hair-spring  dividers ;  genuine  Alteneder  bow 
instruments  and  ruling  pens.  The  price  for  this  set  (1905)  should  be  about  fif- 
teen dollars.  If  the  student  cares  to  pay  the  difference  in  price,  it  is  advisable  to 
substitute  a  compass  with  hair-spring  adjustment  for  that  which  comes  with  the 
above  set. 

A  substitute  for  a  case, 
Fig.  2,  and  better  adapted 
for  carrying  instruments 
in  the  pocket,  may  be 
made  by  the  student.  It 
is  of  chamois  leather  — 
cloth-bound  on  the  edges, 
if  desired  —  and  is  fitted 
with  pockets  of  the  same 
material  to  hold  the  in- 
struments. 

4.  The  Drawing 
Board  (Plate  2)  should  be 
of  well-seasoned,  straight- 
grained  white  pine,  free 
from  sap  and  knots  and 
neither  shellacked  nor  var- 
nished. The  cleats  should 
be  of  the  same  wood, 
tongued  and  grooved,  and 
screwed  to  the  board  — 
never  glued.  To  provide 
for  the  contraction  and  expansion  of  the  board,  due  to  atmospheric  changes,  the 
screws  should  pass  through  slots  in  the  cleat,  having  a  width  equal  to  the  diameter 
of  the  screw  (see  Plate  2).  With  this  arrangement  the  board  is  less  likely  to 
warp  or  split,  since,  while  the  heads  of  the  screws  have  sufficient  bearing  to  hold 
the  cleats  in  place,  the  slots  permit  the  screws  to  move  back  and  forth  in  the 

*See  section  of  the  head  of  the  Alteneder-style  compass,  Plate  i.     Not  all  compasses  having  the 
handle  attached  to  the  head,  as  shown  in  the  cut,  are  necessarily  pivot-joint  instruments. 


Fig.  2. 


Plate 


COMPASSES 

ALTENEDER   STYLE  OLD  STYLE 


COMPASS    PARTS 


RULING 
PEN 


SOCKET    FOR       SOCKET    FOR 
NEEDLE.   POINT  LEAD 


BOW  SPACERS        BOW  PENCIL. 


PRICKER 


(5) 


Plate  2 


TRIANGLES 


DRAWING  BOARD 


0 


SQUARE 


FLAT  SCALE 


SANDPAPER  PAD 


PORTFOLIO 


\\.Aw\vA.A  \ ^ J i \       V       .       \       >       .      \       X       V       \       t       >     \\ 

TRIANGULAR     SCALE 


/  /./../,/  ,/  ,/  ,/  ,/  ,/,/  .1,1,1,1,1.1,1,1,1,1,  1,1,1,1,1:  1,1,1,1,1 ,1,1,  1,1,1,  1,1  ,1,1,1,  1,1, 1,1,  1:1,  1,1:1..,.]  L 

INK    SLAB 

STICK  INDIA  INK 


READING    GLASS 


STEEL  INK    ERASER   (SCALP 


BURNISHER 


IRREGULAR    OR    FRENCH    CURVES 


(7) 


DRAWING  INSTRUMENTS  AND  MATERIALS -- THEIR  SELECTION.        9 

cleats  with  the  expansion  and  contraction  of  the  board.  The  outer  edge  of  each 
cleat  should  be  perfectly  straight,  and  the  grain  of  the  wood  parallel  to  the  edge  of 
the  cleat.  When  purchasing  ask  the  dealer  for  a  steel  straight-edge,  and  with 
it  test  the  straightness  of  the  working  edge  of  the  board.  Another  method  is 
as  follows  :  — 

(#)  To  test  the  straightness  of  the  working  edge  of  a  drawing  board:  Place 
the  board  on  a  sheet  of  paper  laid  flat,  and  upon  it,  using  either  cleat  as  a  straight- 
edge, rule  a  very  narrow  line  the  full  length  of  the  cleat.  Now  swing  the  board 
around  to  reverse  the  ends  of  the  same  cleat  with  respect  to  the  ruled  line,  and 
to  bring  the  same  edge  of  the  cleat  on  to  the  ruled  line.  Rule  again,  and,  if 
the  two  ruled  lines  coincide  throughout,  the  edge  of  the  cleat  may  be  regarded 
as  practically  straight.  The  two  edges  of  each  of  the  two  cleats  should  be 
tested. 

The  'metal  edge  sometimes  attached  to  small  drawing  boards  is  altogether 
unsatisfactory. 

5.  The  T-square  (Plate  2).     The  usual  T-square  is  made  of  pear  wood.     A 
better  one  has  the  so-called  ebony-lined  blade.      For  greatest  accuracy,  a  steel 
T-square  and  a  special  steel  edge  for  the  drawing  board  are  necessary,  although 
this  T-square  tends  to  soil  the  paper  and  to  smear  dry  ink  lines.       In  choosing  a 
T-square,  see  that  the  blade  is  wholly  free  from  nicks  and  that  the  grain  is  straight 
and  parallel  to  the  edges  of  the  blade.     The  straightness  of  the  blade  and  head 
should  be  tested  according  to  a,  Art.  4,  or  by  placing  each  against  a  steel  straight- 
edge held  between  the  eye  and  the  light ;  if  the  contact  is  perfect  throughout,  no 
light  will  be  seen  between  the  edges. 

6.  The  Triangles  (Plate  2)  are  made  of  wood,  hard  rubber,  or  amber.    The  rub- 
ber and  the  amber  triangles  are  more  accurate  than  the  wooden  ones.     The  amber  is 
less  likely  to  soil  the  drawing  than  the  hard  rubber,  and  also  permits  the  lines  of  the 
drawing  to  be  seen  through  the 

triangle  —  often  a  decided  con- 
venience. In  selecting  a  trian- 
gle, sight  across  its  surface  to  see 
that  it  is  not  warped.  To  test  the 
straightness  of  the  edges,  proceed 
according  to  a,  Art.  4,  or  place 
each  edge  against  a  steel  straight- 
edge held  between  the  eye  and 
the  light,  as  described  in  Art.  5.  Fig.  3. 

(a)  To  test  the  90°  angle :  Place  the  triangle  A,  Fig.  3,  against  a  straight- 
edge, and  with  a  very  sharp  pencil  draw  an  accurate  line  along  the  edge  ab.  If, 


io       DRAWING  INSTRUMENTS  AND  MATERIALS  —  THEIR  SELECTION. 


when  the  triangle  is  turned  over,  as  at  A',  edge  ab  does  not  coincide  with  the 

ruled  line,  the  triangle  is  not  "  square." 

(b)     To  test  the  45°  angles :    After  testing  the  T-square  blade,  the  working 

edge  of  the  drawing  board,  and 
the  right  angle  of  the  triangle, 
draw  with  the  T-square  two 
parallel  lines,  ab  and  cd  (Fig. 
4).  With  the  T-square  as 
shown  and  the  triangle  in  posi- 
tion A,  draw  line  ef.  Bring 
the  triangle  to  position  A', 
without  turning  it  over,  and 
draw  gh.  With  the  dividers 
compare  the  length  of  lines  ef 
and  gh;  if  they  are  equal,  the 
45°  angles  are  correct. 


Fig.  4. 


(c)  To  test  the  J0°  and  6cP  angles :  After  testing  the  T-square  blade,  the 
working  edge  of  the  drawing  board,  and  the  right  angle  of  the  triangle,  draw 
with  the  T-square  line  ab  (Fig. 
5).  Move  the  T-square  down 
about  \  inch  to  the  position 
shown;  place  the  triangle  in 
position  A,  and  draw  line  cd. 
Turn  the  triangle  over  to 
position  A',  and  draw  de. 
With  the  dividers,  compare 
the  lengths  of  lines  ce,  cd,  and 
de  ;  if  they  are  all  equal,  the  30° 
and  60°  angles  are  correct. 

7.  The   Scale    (Plate    2) 
should    be    perfectly     straight 

and  free  from  nicks,  all  edges  thin  and  sharp,  and  the  graduations  very  narrow, 
clear-cut  lines.  Blunt  edges  and  blurred  graduations  seriously  interfere  with  accu- 
racy of  measurement. 

8.  The  Pricker  (Plate   i).     A  good  substitute  can   easily   be   made   thus: 
Whittle  out  of  soft,  straight-grained  wood  a  handle  about  3!  inches  long  and  taper- 
ing from  £  inch  to  T3g  inch  in  diameter.     Break  off  the  eye  of  a  No.  9  sewing 
needle,  and  with  a  pair  of  pincers  push  the  point  of  the  needle  into  the  smaller  end 
of  the  handle,  taking  care  to  keep  the  needle  accurately  in  line  with  the  axis  of  the 


Fig.  5- 


Plate  3 


BEAM    COMPASS 


ADJUSTABLE 
T   SQUARE 


SABLE     BRUSH 


CAMEL  HAIR    BRUSHES 


(  A  brush  at  both  ends) 


DRAWING  INSTRUMENTS  AND  MATERIALS  —  THEIR  SELECTION.       13 

handle.  When  the  needle  has  been  pushed  in  about  three-fourths  of  its  length, 
draw  it  out,  reverse  it,  and  force  it  broken  end  first  into  the  hole.  The  needle 
should  project  about  |  of  an  inch. 

9.  The  Thumb  Tacks.     Tacks  costing  from  five  to  twenty  cents  a  dozen  are 
sufficiently  good.     Small  copper  tacks  (not  iron  ones)  are  sometimes  used.     The 
shank  of  a  thumb  tack  should  be  slender,  the  point  sharp,  and  the  head  shallow 
and  sloping  to  a  sharp  edge,  that  it  may  not  catch  the  edge  of  the  T-square  blade. 
The  shank  should  be  so  fastened  to  the  head  that,  when  pressed  into  the  drawing 
board,  it  will  not  push  through  the  head  of  the  tack  into  the  thumb. 

10.  The  Pencils.     The  common  writing  pencil  is  wholly  unfit  for  mechanical 
drawing ;  only  the  best  hexagonal  drawing  pencils  should  be  used. 

11.  The  Pencil  Sharpener  (Plate  2).     A  small,  fine-cut  file  is  often  used  for 
sharpening  pencil  and  compass  leads.     A  convenient  and  inexpensive  substitute  is 
the  sandpaper  pad  (Plate  2).     A  piece  of  fine  sandpaper,  or  emery  cloth  fastened 
to  a  strip  of  wood,  say  6  x  i.]  x  ^  in.,  will  do  very  well. 

12.  The  India  Ink.     The  best  stick  ink  gives  a  glistening,  jet  black  line  and 
is  satisfactory  for  brush  work,  while  lines  made  with  cheap  inks  are  likely  to  look 
dead,  tend  to  smear  easily,  and  are  unsuitable  for  brush  work.     A  stick,  half  size, 
at  fifty  cents,  is  the  cheapest  that  should  be  considered. 

13.  The  Steel  Ink  Eraser.     A  surgeon's  scalpel  is  recommended,  as  the  steel 
is  far  superior  to  that  in  ink  erasers  usually  found  at  the  stationer's.     The  length 
should  be  about  5-*-  in.,  and  the  shape  as  shown  in  Plate  2. 


CHAPTER    II. 

USES   AND   CARE  OF   THE  INSTRUMENTS   AND  MATERIALS  —  MANIPULATION. 

14.  The  following  pages  deal  with  the  technique  and  ^uork^ng  methods  of 
mechanical  drawing,  independent  of  the  principles  of  the  subject,  which  are  covered 
by  the  descriptive  geometry. 

The  study  of  technique  is  principally  concerned  with  the  training  of  the 
several  sense  powers  —  manual  skill,  correct  observation,  speed,  judgment,  and 
taste  —  which  must  underlie  the  operations  of  the  expert  all-around  draftsman. 

Working  methods  are  those  dependent  upon  knowledge  rather  than  upon  the 
sense  powers,  and,  especially,  upon  experience  with  the  needs  and  necessities  of 
professional  practice.  The  term  also  serves  to  distinguish  directly  effective  and 
practical  methods  from  those  which  are  purely  educational. 

The  methods  here  presented  are  not  set  forth  as  the  only  ones  of  value. 
Draftsmen  often  differ  in  their  opinion  of  modes  of  procedure,  influenced  naturally 
by  their  individual  experience  or  by  the  traditions  and  character  of  the  work  of  a 
particular  office.  A  beginner,  however,  should  take  pains  to  carry  out  instructions 
literally  until,  having  learned  to  work  according  to  the  methods  indicated,  he 
reaches  a  point  where  he  is  competent  to  judge  other  methods. 

Success  in  mechanical  drawing  rests  largely  on  personal  attention  to  many 
details.  The  advantage  of  workmanlike  habits  should  be  kept  in  mind.  Avoid 
lounging  on  the  drawing  table,  and  other  lazy  habits.  Quiet,  brisk  attention  to 
the  work  in  hand  is  not  only  suggestive  of  one's  personal  quality,  but  is  also  con- 
ducive to  better  results  in  drawing.  Keep  the  instruments  and  materials  in  orderly 
arrangement  on  the  table,  not  only  for  the  sake  of  appearance,  but  also  to  avoid 
loss  of  time  in  searching  for  the  thing  needed. 

The  explanations  and  directions  concerning  the  uses  and  care  of  the  instru- 
ments should  receive  close  attention.  It  is  not  sufficient  merely  to  read  the  text, 
but  this  reading  should  be  supplemented  by  an  immediate  examination  of  the  in- 
strument or  article  considered.  The  names  of  the  instruments  and  their  parts 
(Plates  i,  2,  and  3)  should  be  remembered.  In  the  directions  for  manipulation, 
the  processes  must  not  be  deferred  until  the  regular  exercises  are  begun,  but  each 
must  be  practiced  at  once  and  exactly  as  described.  A  great  deal  can  be  learned  by 

(14) 


THE  CARE  OF  THE  INSTRUMENTS  AND  MATERIALS.  15 

experimenting  with  the  instruments  and  materials,  and  through  practice  before  be- 
ginning to  work  on  a  finished  drawing. 

15.  The  Care  of  the  Instruments  and  Materials.  Keep  the  instruments 
clean,  free  from  moisture,  and  always  in  working  order.  The  pens  should  be 
sharpened  properly,  and  must  not  become  clogged  with  ink.  The  compass  joints 
should  work  freely  without  being  either  loose  or  stiff.  A  drop  of  oil  may  be  used 
on  the  regulating  screws  of  the  pens  and  bow  instruments,  should  they  not  turn 
easily.  Do  not  use  short  leads  or  blunt  needle  points  in  the  compass  and  bow 
pencil.  In  opening  and  closing  the  bows,  pinch  the  legs  together  to  release  the 
pressure  on  the  regulating  nut  (A,  Fig.  6),  then  turn  the 
nut,  and  let  the  leg  spring  gently  back.  When  not  in  use, 
the  bow  instruments  and  the  blades  of  the  pens  should  be 
left  open  (A,  Fig.  7),  and  the  instruments  slightly  oiled, 
occasionally,  with  a  soft  cloth. 

Wood  is  more  likely  to  warp  when  one  side  only  is  ex- 


posed  to  the  air ;  hence,  the  drawing  board  should  be  left 
standing  on  edge,  that  air  may  circulate  about  it,  or,  if  left 
on  the  drawing  table,  it  should  be  closely  covered.     When     f| 
not  in  use,  the  T-square  and  triangles  should  be  hung  up, 
and  away  from  heating  apparatus  and  sunlight. 

Test,  from  time  to  time,  the  working  edge  and  surface 
of  the  drawing  board,  and  the  edges  of  the  T-square,  and 


Fie-  6  triangles  (Arts.  4,    5,  and  6) ;    if  found  inaccurate,   they         A 

should  be  sent  to  a  cabinet  or  pattern  maker  to  be  trued. 

If  the  drawing  board  is  planed  off  to  remove  dents,  it  should  be  planed  on  both 
sides,  since  it  is  more  likely  to  warp  if  planed  on  one  side  only. 

The  best  of  care  should  be  taken  of  drawing  papers  and  of  drawings,  both 
finished  and  unfinished,  all  of  which  should  be  kept  flat  in  a  portfolio  or  stiff  paper 
cover.  The  stick  of  ink  should  be  nicely  wrapped  with  paper,  glued  to  the  ink,  to 
prevent  breaking. 

16.  Drawing  Papers.  The  paper  best  suited  for  a  drawing  depends  upon  the 
amount  and  character  of  the  proposed  rendering  (Art.  34).  In  selecting  a  paper,  it 
may  be  necessary  to  take  into  account  its  surface  —  whether  hard  or  soft,  smooth 
or  rough, —  and  its  interior  quality  —  whether  comparatively  soft,  or  hard  and  of 
uniform  texture.  The  Whatman  papers  are  especially  satisfactory  for  finished  and 
display  drawing.  This  paper  comes  only  in  sheets,  of  various  weights  and  sizes  (see 
the  end  of  this  paragraph),  and  is  finished  in  three  different  styles  of  surface  — 
hot  pressed,  cold  pressed,  and  rough.  In  a  line  drawing  which  is  to  be  inked,  which 
will  require  considerable  time  to  finish,  and  which  is  likely  to  be  subjected  to  fre- 
quent erasure  or  hard  usage,  the  paper  should  have  a  very  smooth  surface  and  be  of 


16  DRAWING  PAPERS — TRACING  PAPER  —  TRACING  CLOTH. 

uniformly  hard  texture  throughout  —  qualities  found  in  the  "normal"  paper. 
For  precise  line  drawing,  in  pencil  or  ink,  without  excessive  erasure  or  very  hard 
usage,  Whatman's  hot  pressed  and  linen  record  papers  are  suitable ;  the  former 
stands  erasure  better  than  the  latter,  but  the  latter  has  the  smoother  surface.  For 
working  drawings,  and  drawings  to  be  traced,  an  inexpensive  but  fairly  hard  paper, 
such  as  the  "  duplex,"  may  be  used.  This  paper  is  sold  in  sheets,  by  the  yard,  or  in 
ten-yard  rolls,  and  in  widths  of  30,  36,  42,  56,  and  62  inches.  It  comes  in  two  tints, 
cream  and  drab,  which  may  be  less  trying  to  the  eyes  than  a  white  paper.  When 
blue  prints  are  to  be  made  directly  from  the  drawing,  a  hard  bond  paper  (Crane's, 
for  example)  is  preferable.  Wash  drawings  must  be  made  on  Whatman's  cold 
pressed  or  on  a  water-color  paper.  Useful  for  practice  work  and  cheaper  than  the 
preceding  are  the  German  papers,  the  American  imitations,  and  Manila  paper. 
Besides  the  above-mentioned  papers  there  are  many  others,  for  a  description  of 
which  the  reader  is  referred  to  the  dealer's  catalogue. 

Standard  sizes  of  Whatman  drawing  papers  :  — 

Cap,  13x17  inches.  Super  Royal,  19  x  27  in. 

Demy,  15  x  20  in.  Imperial,  22  x  30  in. 

Medium,  17  x  22  in.  Atlas,  26  x  34  in. 

Royal,  19  x  24  in.  Double  Elephant,  27  x  40  in. 

Antiquarian,  31  x  53  in. 

Whatman's  extra  heavy,  normal,  duplex,  and  bond  papers  come  only  in  the 
royal,  imperial,  and  double  elephant  sizes. 

The  better  side  of  a  drawing  paper  is  indicated  by  its  water  mark.  Therefore, 
in  cutting  up  a  sheet,  keep  track  of  the  better  side  by  putting  some  distinguishing 
mark  on  the  opposite  side. 

17.  Tracing  Paper  ;  Tracing  Cloth.  For  temporary  drawings,  for  transfers,  and 
in  planning,  tracing  paper  is  well-nigh  indispensable.  Tracings  for  blue  prints,  and 
tracings  required  to  stand  handling  and  ink  erasure  should  be  made  on  tracing  cloth. 

The  dull  surface  of  the  cloth  is  better  for  pencil  or  pen.  A  wash  of  India  ink 
or  color  may  be  used  on  the  dull  surface,  if  sparingly  applied,  but  the  cloth  will 
cockle  more  or  less.  If  a  color  wash  is  used,  inking  should  be  done  on  the  opposite 
or  glazed  side  of  the  cloth.  (Colored  crayon  works  better  on  tracing  cloth  than  a 
wash,  and  is  growing  in  favor ;  the  crayon  should  be  evenly  applied  to  the  dull  sur- 
face, and,  if  preferred,  may  be  worked  flat  with  a  stump.)  The  glazed  surface  of 
the  cloth  is  adapted  only  for  inking,  although  many  prefer  the  dull  surface  for  this 
work.  When  the  surface  does  not  take  the  ink  satisfactorily,  it  should  be  cleansed 
with  soft  paper  or  sprinkled  with  powdered  chalk  (scraped  from  blackboard 
crayon) .  Rub  the  chalk  lightly  into  the  surface,  and  dust  off  thoroughly.  As 
tracing  cloth  is  very  susceptible  to  moisture,  which  stretches  it,  the  cloth  should 
not  be  used  when  permanent  accuracy  of  drawing  is  required. 


DRAWING  PENCILS. 


1 8.  Pencils.     Ruled  pencil  lines  should  be  legible,  easy  to  erase,  and  unac- 
companied by  grooves  in  the  paper.     To  satisfy  these  conditions,  it  is  necessary 
not  only  to  manage  the  pencil  properly,  but  to  see  that  the  grade  of  the  pencil 
is  adapted  to  the  surface  and  texture  of  the  paper. 

In   precise    drawing  —  geometrical    con- 
struction,   for    example  —  rendered    in  very 

A 

narrow,  light  lines  on  a  paper  hard  through- 
out and  having  either  a  smooth  or  a  rough 
surface,  there  should  be  used  a  6H  pencil 
sharpened  to  a  ruling  point  (a,  Art.  19).  If 
greater  distinctness  of  line  is  required  — 
as,  for  example,  when  a  drawing  is  to  be 
traced  —  a  2H  to  4H  pencil  is  best.  If  a 
surface  grooves  easily,  as  is  the  case  with 
Bristol  board  and  bond  paper,  which  have  a 
hard  surface,  but  are  soft  beneath,  it  is  best 
to  use  an  HB  or  F  pencil.  For  sketching 
(in  mechanical  drawing),  for  suggesting  letter- 
ing, and  for  lining  in  finished  pencil  drawings, 
there  should  be  used  an  H  pencil  with  a  some- 
what blunt,  conical  point. 

The  following  list  gives  a  very  general  idea  of  the  grades  of  pencil  suitable 
for  the  papers  mentioned  in  Art.   16:  — 

Whatman's  Hot  Pressed,  H  to  6H. 

Whatman's  Cold  Pressed,  for  outline  draw- 
ing, 6H  ;  for  wash  drawing,  HB  to  3H. 

Normal,  H  to  8H. 

Water  Color,  HB  to  ^H. 

Linen  Record,  H  to  4H. 

Duplex,  sH  to  6H. 

Bond,  HB  to  H. 

Bristol  Board,  HB  to  H. 

19.  The  Sharpening  of  Pencils  and  Compass 
Leads.       (a)        The  ruling  point.        Cut    away 
the  wood  of   the  pencil  to  expose  at  least  half 
an  inch    of   the   lead    (A,    Fig.    8).     With  the 
file    or    sandpaper   pad    resting    on    something 
solid,  as   the  edge   of   the   drawing   table,  and 

with   the   forefinger  on   the   wood  where  it  meets  the  lead   (Fig.    9),  press  the 
lead  lightly  but  firmly  against   the    sandpaper,  and  with  a  steady  back-and-forth 


Fig.  8. 


Fig.  9. 


i8 


THE  SHARPENING  OF  PENCILS  AND  COMPASS  LEADS. 


Fig.  10. 


motion  grind  opposite  sides  of  the  lead  to  form  an  accurate  wedge  (see  side  view 
B,  Fig.  8,  and  edge  view  C).     Next,  holding  the  pencil  as  in  Fig.  10,  carry  it  very 

lightly  back  and  forth,  and  with 
each  separate  stroke  slightly  rotate 
the  pencil  about  its  axis  in  the  op- 
posite direction  to  that  of  the  stroke. 
This  rocking  motion  forms  the 
finished  point  (D  and  E,  Fig  8). 
It  will  be  noted  that,  seen  side- 
wise,  the  contour  of  the  point  is 
elliptical  (D,  Fig.  8)  ;  a  cross  sec- 
tion of  the  point  gives  the  form 
shown  at  ab,  D,  Fig.  8.  The  advantage  of  this  ruling  point  is  that,  by  slightly 
changing  the  angle  of  the  pencil,  when  ruling  each  new  line,  the  pencil  will  rest 
on  a  perfectly  sharp  portion  of  its  point. 

Another  ruling  point  sometimes  used,  is  formed  by  first  making  a  conical  point 
(F,  Fig.  8)  and  then  grinding  its  opposite  sides  to  form  a  wedge. 

(b)  The  measuring  point.     This  point,  which  is  used  to  lay  off  measurements 
from  the  scale,  is  formed  by  working  the  lead  to  a  slender  and  extremely  sharp 
conical  point  (F,  Fig.  8).     When  forming  this  point,  carry  the  lead  back  and  forth 
on  the  sandpaper,  meanwhile  constantly  rotating  the  pencil  about  its  axis. 

It  is  convenient  to  have  the  opposite  ends  of  the  same  pencil  sharpened 
for  ruling  and  measuring  points,  in  which  case  the  letter  representing  the 
grade  of  the  pencil  should  be  scratched  or  cut  at  the  middle  of  the  pencil. 

(c)  The  sketching  point.     This  point  is  used  for  putting  in  an 
occasional  freehand  line  on  the  mechanical  drawing,  for  sketching  in 
lettering,  writing  on  the  drawing,  etc.     It  should  be  conical  in  form, 
less   slender  than  the  point  F,  Fig.   8,   and  only  fairly  sharp.     For 
this  purpose  an  H  or  HH  pencil  may  be  used. 

(d)  Compass  leads.     The  leads  for  the  compass  and  bow  com- 
pass should  be  placed  in  the  sockets  of  these  instruments  and  then 
sharpened.     Let  the  lead  extend  well  beyond  the  socket  of  the  in- 
strument, that   the  latter  may  not  come   in  contact  with  the  sand- 
paper.    Form   the  point  according  to  the   directions  for  forming  a 
ruling   point  (see  a).     When  sharpened,  the  lead  should  be  adjusted 
in  the  socket  thus :   Place  the  pen  in  the  compass,  set  the  needle 
point  of  the  compass  to  correspond  with  the  point  of  the  pen,  and 
then  set    the   lead    to   correspond   with    the    needle  point.     When 


Fig.  n. 


the  compass  is  closed    (Fig.   n),  the  needle   should  project  slightly  beyond  the 
tip  of   the   lead  or  pen  (see  the   distance  in  Fig.    n).     When  the   compass  is 


.  THE  PRICKER  —  THE  T-SQUARE. 


open  (Fig.  12),  the  plane  ab  of  the  lead  should  be  perpendicular  to  a  plane  pass- 
ing through  the  axes  cd  and  ef  of  the  legs. 

20.  The  Pricker  ;  its  Use  in  Duplicating 
Drawings.     The  pricker  is  used  to  define  line 
intersections,  to  lay  off  measurements  from 
the   scale,  and  in   duplicating   drawings.     A 
fine  needle  should  be  used,  and  immediately 
replaced   when    the    point    becomes    at    all 
blunted. 

(a)  In  using  the  pricker,  hold  it  per- 
pendicular  to   the  paper   (Fig.    13).     When 
defining  a  point  in  the  drawing,  do  not  force 
the  point  of   the  needle   through  the  paper, 
but   make   an    indentation    which    is   barely 
visible.     In  order  that  such  a  point  may  be 
readily  found  again,  enclose  it  in  a  small  free- 
hand circle. 

(b]  Diagrams,  maps,  photographs,  etc., 
are   sometimes   duplicated   as  follows :  Place 
the  original  over   one   or  more  fresh  sheets 
of  paper,  according  to  the  number  of  dupli- 
cates required.     Prick    the    essential   points 
in  the  original  through  to  the  sheets  beneath 
it,  and  connect  the  points  as  in  the  original. 

Take  special  care  to  hold  the  pricker  perpen-  &•  I2< 

dicular  to  the  paper.  As  a  safeguard  against  connecting  wrong  points,  before  con- 
necting the  points  draw  a  freehand  circle  about  each  point,  and  letter  or  number  a 
few  of  the  more  important  ones. 

21.  The  T-square  ;  Straight  Line  Ruling.     The   T-square  is  used  in   ruling 

horizontal  lines,  and  in  combination  with  the  triangles 
(Art.  23). 

(a)  To  rule  a  horizontal  line.  Hold  the 
T-square  as  shown  in  Fig.  14,  press  its  head  firmly 
against  the  left-hand  cleat  of  the  drawing  board,  and 
the  blade  flat  against  the  paper.  Incline  the  pencil 
to  the  right  (Fig.  15),  and  slightly  away  from  the 
T-square  blade  (Fig.  16),  so  that  the  surface  of  the 
ruling  point  (D,  Fig.  8)  will  bear  against  the  blade,  and  the  edge  of  the  point  lie 
in  the  line  of  contact  of  the  edge  of  the  T-square  blade  and  the  paper.  Let  the 


Fig.  13- 


20 


THE  STRAIGHT-EDGE  —  THE  TRIANGLES. 


fingers  rest  on  the  T-square  blade  (Fig.  15),  press  the  pencil  firmly  but  lightly  on 
the  paper,  and  carry  it  steadily  from  left  to  right,  keeping  the  pressure  uniform, 

and  do  not  change  the 
initial  position  of  the 
pencil. 

22.  The  Straight- 
edge. This  is  a  special 
ruler,  similar  to  the  T-- 
square blade,  and  used 
most,  perhaps,  in  sur- 
veying and  engineering. 
It  is  of  wood,  hard  rub- 
ber, or  steel,  and  made 
in  various  lengths  from 
12  inches  to  120  inches. 
(«)  To  draiv  ac- 
curately a  line  longer 
than  the  straight-edge, 
or  any  especially  long 
line :  Stretch  taut  a  fine  silk  thread  between  the  points  which  mark  the  ends  of 
the  required  line  ;  prick  off  carefully  one  or  more  intermediate  points  in  the  thread, 
and  connect  the  points  by  means  of  a  steel  straight-edge. 


Fig.  15. 


b 
Fig.  1 6. 


23.     The  Triangles  are  used  as  rulers,  to  obtain  parallel  lines,  and  to  draw 
lines  making  certain  angles,  as  shown  in  the  following  pages. 


USE    OF    THE    T-SQUARE    AND    TRIANGLES. 


21 


TRIANGLE  AND  T-SQUARE  COMBINATIONS.  (a)  To  rule  a  vertical  line. 
Place  the  T-square  as  in  drawing  a  horizontal  line.  With  the  left  hand,  hold 
the  head  of  the 
T  -  square  firmly 
against  the  edge 
of  the  drawing 
board,  and  then 
slide  the  hand 
from  the  head  of 
the  T-square  along 
the  blade  to  keep 
it  in  position. 
Place  the  triangle 
with  the  right  hand 
(Fig.  17),  and  hold 
it  in  position  with 
two  fingers  of  the 
left  hand  —  which 
also  steadies  the 
T-square  blade  — 
that  the  right  hand 

shall  be  free  to  manage   the  pencil.     Guide  the  pencil  away  from  the  T-square 
rather  than  toward  it. 

(3)      To  draiv  lines  making  angles  of   15°,    30°,  45°,  60°,  and  75°  with  the 


Fig.  17- 


Fig.  1 8. 


Fig.  19. 


horizontal.     Place    the    T-square    and    triangles    as  shown   in  Figs.    18,    19,   20, 
and  21. 


22 


USE    OF   THE    T-SQUARE    AND    TRIANGLES. 


To  draw  a  perpendicular  to  a  line  which  makes  an  angle  of  45°,  30°,  or  60°, 
reverse  the  triangle,  as  shown  in  Fig.  20.     It  will  be  seen  (Fig.  21)  that  the  tri- 


\ 


Fig.  20. 


Fig.  21. 


angle  which  makes  an  angle  of  75°  with  the  horizontal  A  must  make  an  angle  of 
15°  with  the  vertical  B. 

In  drawing  a  line  from  a  given  point  in  a  line,  as  point  C  in  line  AC  (Fig.  19), 
do  not  fit  the  T-square  to  the  line,  as  at  A'C,  and  then  attempt  to  place  the 
corner  of  the  triangle  at  the  given  point,  as  shown  at  Cf,  but  keep  the  T-square 
blade  away  from  the  given  line,  A  C,  that  the  edge  of  the  triangle  shall  pass  through 
the  given  point. 

TRIANGLE  COMBINATIONS,  (c)  To  draw  lines  parallel  or  perpendicular  to 
an  oblique  line,  or  making  with  it  angles  of  15°,  30°,  45°,  60°,  and  75°. 

Let  it  be  required  to  draw  through  point  C  (Fig.   22)   a  line  parallel  to  a 


Fig.  22. 

given  line,  as  AB.     Fit  accurately  to  the  given  line  an  edge  of  either  triangle,  as 
M,  and  place  against  it  another  triangle,  as  N.     Hold  N  firmly  in  place  with  the 


USE  OF  THE  TRIANGLES. 


Fig-  23- 

left  hand,  L,  and  slide  the  triangle  M  along  N  to  position  M'  t  with  its  edge  pass- 
ing through  the  given  point  C.     Keep  M'  and  N  firmly  in  position  with  the  left 
hand,  to  free  the  right  hand  for  drawing  the  required  line,  as  from  E  through  C  to  D. 
Positions  of  the  triangles  for  drawing  a  perpendicular  to  an  oblique  line,  and  for 


24  THE  PROTRACTOR  —  THE  FRENCH  CURVE. 

drawing  lines  making  with  an  oblique  line  any  of  the  above-stated  angles,  are 
shown  in  Fig.  23.  The  solid  black  represents  a  fixed  triangle,  and  the  dash-and- 
dot,  a  movable  triangle  set  upon  the  given  line.  The  full  line  —  representing  the 
triangle  which  guides  the  pencil  —  shows  either  a  new  position  of  the  movable 
triangle  (A,  B,  Dt  Et  F,  G,  and  H},  or  the  position  of  a  triangle  substituted  for  it 
(J,  K,  Lt  and  M}.  The  method  C,  Fig.  23,  which  uses  two  movable  triangles, 
is  occasionally  more  convenient,  although  less  direct  than  the  other  methods  that 
give  the  same  results. 

24.  The  Protractor.     This  instrument,  used  for  laying  off  angles,  is  a  semi- 
circular disc  of  metal,  horn,  or   cardboard,  divided  into  degrees,  half  and  quarter 
degrees.     Metal  protractors  with  a  vernier  attachment  read  to  one  minute. 

25.  The  French  Curve ;  the  Template ;  Curved  Line  Ruling.      Curved    rulers 
are  made  of  hard  rubber,  wood,  or  celluloid,  and  include  the  French  curve  (Plate 


Fig.  24. 

2),  the  railroad  curve,  the  ship  curve,  and  the  spline.  There  is  also  a  patent  ad- 
justable curve  made  of  rubber  combined  with  soft  lead.  The  spline  and  adjustable 
curves  may  be  bent  to  fit  fairly  flat  curves  up  to  60  inches  or  more  in  length. 

(a)  The  use  of  the  French  curve.  Having  located  the  points  in  a  curve,  con- 
nect them  by  a  freehand  line  sketched  lightly  with  a  3H  or  4H  pencil.  This  line 
should  pass  accurately  through  the  located  points  and  at  the  same  time  present 
a  curve  as  graceful  as  possible.  The  line  should  be  sketched  without  excessive 
erasure,  because  this  tends  to  obscure  or  wholly  to  obliterate  the  located  points 
unless  they  have  been  defined  with  the  pricker  (a,  Art.  20).  The  final  line,  whether 
drawn  in  pencil  or  in  ink,  should  be  ruled  by  means  of  one  or  more  French  curves, 
as  follows :  — 

Let  BCD  (Fig.  24)  be  a  series  of  points  connected  freehand.  Find  by  trial 
the  portion  of  a  French  curve  which  will  coincide  with  or  fit  the  sketched  line, 


THE  TEMPLATE  —  SCALES. 


and  for  as  long  a  distance  as  possible.  Rule  the  line  ;  find  a  curve  which  will  fit 
another  succeeding  portion  of  the  sketched  line,  rule  again,  and  continue  the 
process  until  the  whole  line  is  thus  ruled  in  sections.  In  order  to  insure  smooth- 
ness of  curvature  in  the  line  as  a  whole,  in  ruling  each  succeeding  section  the 
French  curve  must  be  fitted  back  some  distance  on  the  preceding  (inked)  section. 
For  the  same  reason,  in  ruling  each  section,  the  line  should  stop  a  little  short  of 
the  full  length  of  the  section.  These  requirements  are  illustrated  in  Fig.  24. 
Curve  A  fits  section  BG  of  the  sketched  curve  BCD,  but  the  ink  line  is  carried 
only  from  B  to  F.  Curve  A'  fits  section  GK,  and  also  fits  back  on  section  BG  to 
include  portion  EF  already  inked.  The  ink  line  is  carried  from  F  to  J;  that  is, 
distance  JK  short  of  the  full  length  of  section  GK.  Curve  A"  fits  back  on  section 
GK  to  H,  which  includes  portion  HJ  already  ruled,  and  forward  to  point  M.  The 
inked  line  is  carried  from  J  to  L. 

In  rilling  a  curve,  the  pen  should  be  lie  Id  perpendicular  to  the  paper  (Fig.  2$),  so 
that,  when  carried  around  sharply  curving  portions  of  the  French  curve,  it  may 
turn  easily  on  its  point. 

(b]  The  template.  This  is  a  substitute 
for  the  French  curve  —  made  by  the  draftsman  — 
and  used  either  as  a  time-saving  device  or  when 
the  French  curve  cannot  be  fitted  to  the  given 
points.  It  is  made  of  thin  sheet  metal,  wood, 
rubber,  or  thick  celluloid.  If  thin  wood  is  used, 
the  required  curve  may  be  drawn  directly  on  it. 
In  the  case  of  rubber  or  celluloid,  the  curve  should 
be  traced  and  then  transferred  to  the  rubber  by 
pricking  through  the  points.  The  template 
should  be  roughed  out  with  a  knife  or  hand  fret- 
saw, shaped  more  accurately  with  a  coarse  file, 
and  finished  with  a  fine  file. 

26.  Scales.  If  the  measurements  of  a  drawing  are  the  same  as  those  of 
the  object  represented,  it  is  said  to  be  "full  size."  A  drawing  is  said  to  be  drawn 
to  a  scale  when,  for  convenience  or  from  necessity,  it  is  made  smaller  or  larger 
than  the  thing  represented.  For  example,  a  map  of  the  United  States  may  be 
drawn  to  a  scale  of  i  inch  =  400  miles ;  surveyors'  plans,  to  scales  of  50  feet  to  the 
inch,  80  feet  to  the  inch,  and  so  forth.  Drawings  of  objects  are  commonly  made  half 
size ;  quarter  size,  or  3  inches  to  the  foot  (written  3  in.  =  i  ft.)  ;  eighth  size,  or  i| 
inches  to  the  foot  (i|  in.  =  i  ft.),  etc.  Of  the  various  drawing  scales  manu- 
factured, it  is  necessary  to  describe  but  two,  the  1 2-inch  architect's  scale,  divided 
as  stated  in  the  list  of  materials  (Art.  2),  and  the  1 2-inch  engineers  scale,  divided 
to  10,  20,  30,  40,  50,  and  60  feet  to  the  inch. 


Fig.  25. 


26 


READING  THE  SCALE. 


(a)    The  architect's  scale.     One  face  of  this  scale  is  divided  into  inches  and  six- 
teenths of  an  inch,  like  the  common  foot  rule,  and  is  used  in  making  full-size  draw- 
ings.   On  each  side  of  the  other  five  faces  there  are  two 
scales,  one  being  one-half  of  the  other.     To  illustrate 
the  arrangement  and  reading  of  the  several  scales, 
consider  the  scale  of  i  in.  =  i  ft.  (Figs.  26  and  27). 
The   denomination  of   the  scale  is  indicated  by  the 
26.  numeral  "  i  "  placed  at  its  right-hand  end.     The  scale 

is  divided  into  12  equal  parts,  each  representing  i 
foot,  and  the  last  one,  CD,  Fig.  27,  is  divided  into  24  equal  parts,  representing  inches 
and  half  inches ;  that  is,  this  i  inch,  representing  i  foot,  is  divided  proportionally 


N         O 

>              1 

•        C              ;          F                       0                        H 

c                        IDA 

y* 

"1"  j"l"l 
0 

; 

20 

3                A               9 

1 

'11                                                       10                                                        9 

1                                                 0 

Fig.  27. 

to  a  foot  rule,  except  that  the  smaller  divisions  are  omitted.  Beginning  at  the  zero 
(under  C}  and  reading  to  the  right,  groups  of  3  inches  each  are  indicated  by  the 
numerals  "  3,"  "  6,"  and  "  9."  Reading  from  the  zero  to  the  left,  feet  are  indicated 
by  the  numerals,  as  "  i,"  "  9,"  "  10,"  and  "  1 1,"  placed  on  the  concave  surface  im- 
mediately below  the  face  of  the  scale. 

To  read  a  measurement.  Let  it  be  required  to  measure  the  line  OP,  Fig.  27. 
The  scale  must  be  placed  so  that  the  feet  and  inches  can  be  read  continuously  with- 
out moving  the  scale.  On  applying  the  scale  to  the  given  line,  it  will  be  quickly 
seen  that  the  line  contains  feet  and  inches ;  in  this  case,  the  graduation  line  "  i  " 
(under  L)  must  fall  on  the  point  O;  the  length  of  OP  is  i  ft.  7|  in.  In  the 
scale  1  in.  =  i  ft.  (Fig.  27),  it  will  be  seen  that  the  smallest  divisions  of  EF  (=  i 
inch)  represent  inches,  and  that  these  read  from  the  zero  (under  F)  to  the  left. 
The  feet  are  read  from  the  zero  to  the  right.  The  line  MN,  read  from  this  scale, 
measures  3  ft.  5  in. 

(b]      The  engineers  scale.     The  face  (Fig.  28)  selected  to  illustrate  the  several 


A  a 


Fig.    28. 

graduations  of  this  scale  is  divided  into  600  equal  parts.     Each  inch  is  therefore 
divided  into  50  equal  parts,  each  representing   i  foot,  and  the  scale  is  said  to  be  50 


THE  COMPASS. 


27 


feet  to  an  inch,  indicated  by  the  "  50  "  (under  F)  stamped  on  the  scale.  It  will  be 
seen  that  groups  of  five  divisions,  as  AB  (Fig.  28),  and  of  ten  divisions,  as  DE,  are 
denoted  by  the  greater  length  of  the  graduation  lines,  and  that  each  group  of 
twenty  divisions  is  indicated  by  a  numeral  stamped  on  the  scale  —  as  the  "2"  oppo- 
site C,  which  is  read  20  feet.  It  will  also  be  seen  that  inches  are  not  distinguished 
by  number  ;  if  required,  these  must  be  found  by  means  of  the  group  divisions  and 
numbers.  Thus,  for  example,  reading  from  the  left-hand  end  of  the  scale,  I  in.  is 
obtained  by  taking  the  graduation  line,  E,  midway  between  the  "4"  and  the  "6." 

To  find  readily  the  face  of  the  scale  in  use,  a  guard  (see  Fig.  26)  is  convenient. 

The  scale  should  never  be  used  as  a  ruler. 

27.  The  Compass —  Large  circles  and  circular  arcs  are  drawn,  according  to 
length  of  radius,  with  the  compass,  the  compass  with  the  extension  bar,  or  the 
beam  compass. 

For  small  circles,  of  |  inch  radius  or  less,  the  bow  compass  should  be  used. 


Fig.  29. 


Fig.  30. 


Fig.  31. 


Use  the  shoulder  tip  of  the  needle  point  (Plate  i),  and  have  the  lead  of  the  com- 
pass sharpened  and  adjusted  in  the  socket  according  to  d,  Art.  19.  For  drawing 
very  small  circles,  the  inside  of  the  needle  point  should  be  beveled. 

(a)  To  describe  a  circle.  Set  the  compass  to  an  approximate  radius,  with  the 
legs  bent  to  bring  each  perpendicular  to  the  paper  (Fig.  12),  and  then  set  it  to  the 
exact  radius.  Holding  the  head  of  the  compass  with  the  tips  of  the  thumb  and 
first  two  fingers  (Fig.  29),  with  the  needle  point  merely  resting  on  the  paper,  start 
the  circle  at  point  A,  under  the  inner  edge  of  the  wrist,  and  describe  a  circle  with 
one  continuous  sweep  of  the  lead.  In  describing  a  circle,  incline  the  head  of  the 
compass  slightly  forward  in  the  direction  of  its  motion  —  indicated  by  the  arrows, 
Figs.  29,  30,  and  31, —  and  guide  the  instrument  by  a  combined  finger,  wrist,  and 


28 


THE  COMPASS. 


arm  movement,  during  which  the  head  of  the  instrument  should  roll  between  the 
thumb  and  forefinger  (Figs.  29-31).  Do  not  acquire  the  habit  of  carrying  the 
lead  back  and  forth  over  a  circle ;  once  drawn,  let  the  circle  stand  —  improvement 
should  come  from  practice,  and  not  from  going  over  or  patching  a  line.  If  a  darker 


8     V 


o 


Fig.  34- 


Fig.  32.  Fig.  33. 

line  is  required,  change  to  a  softer  lead.     Furthermore,  do  not  thrust  the  needle 
point  into  the  paper,  but  give  it  only  sufficient  pressure  to  keep  it  from  slipping. 

The  need  of  bending  the  needle-point  leg  and  of  inclining  the  compass  but 
slightly  in  describing  a  circle  is  shown  in  Figs.  32  and  33.  When  the  needle  point 
is  perpendicular  to  the  paper  (A,  Fig.  32),  if  the  paper  is  accidentally  punctured, 
the  center  thus  made  will  have  a  diameter,  a'bf,  equal  only  to  the  diameter,  ab,  of 
the  needle  point.  If,  however,  the  needle  point  is  inclined,  as  in  A,  Fig.  33,  the 


Fig.  35. 

swinging  of  the  compass  will  cause  the  needle  point  to  ream  out  the  center,  and 
thus  prohibit  its  further  use  for  accurate  work. 

Never  use  the  compass  as  shown  in  Fig.  34. 

(b)     The  lengthening  bar.     When  the  lengthening  bar  (Fig.  35)  is  used,  the 


THE  BEAM   COMPASS  —  THE  DIVIDERS  — -  THE  Bow  SPACERS.      29 

compass  is  likely  to  spring  under  pressure ;  hence  it  must  be  handled  lightly. 
Bend  the  legs  to  bring  them  perpendicular  to  the  paper,  incline  the  instrument 
slightly  in  the  direction  of  its  motion,  and  at  the  beginning  and  the  end  of  the 
line  guide  the  describing  leg  with  a  finger  of  the  left  hand. 

28.  The  Beam  Compass.     This  instrument  (Plate  3)  is  practically  a  compass 
with  a  separated  head  (A  and  B,  Plate  3)  which  slides  on  a  wooden  bar.     Slight 
corrections  of  distance  between  the  legs  of  the  compass  may  be  made  by  means  of 
a  spring  which  is  regulated  by  the  nut  C. 

29.  The  Hair-spring  Dividers  ;  the  Bow  Spacers.     The  hair-spring  dividers  and 
the  bow  spacers  (Plate  I )  are  used  to  transfer  distances,  and  to  space  or  divide  lines 
into  equal  parts.     The  points  of  the  instruments  should  be  very  sharp,  of  exactly 
the  same  length,  and,  when  closed,  should  come  together  accurately.     If  the  points 
are  blunted  or  of  unequal  length,  the  defect  should  be  remedied  on  the  oil  stone. 

(a)     Spacing.     Before  commencing  to  space,  ascertain  the  range  (BC,  Fig. 
36)  of  the  hair-spring  leg  by  turning  the  screw  E,  and  then  set  the  point  of  the  leg 
at  A  midway  between  B  and  C,  so  that  the  leg  may  be 
moved  by  means  of  the  hair  spring  in  either  direction  ac- 
cording to  need.     Let  it  be  required,  for  example,  to  divide 
line  D' B'  (Fig.  37)  into  13  equal  parts.     Moving  the  legs 
by  means  of  the  head  joint,  set  the  dividers  approximately 
equal  to  -Jg-  D'  B' ;  then,  starting  with  one  leg  of  the  di- 
viders placed  at  D',  step  along  the  given  line  until  the 
1 3  spaces  are  laid  off.     If,  on  laying  off  the  last,  or   1 3th, 
space,  the  leg  of   the  dividers  extends  beyond  the  given 
line,  as  distance  B'Avii,  the  assumed   distance  in    the  di- 
viders  must  be  decreased  by  -jL-  of  the  excess,  B' Av",  de- 
termined by  judgment.     If,  however,  on   laying  off  the   I3th  space,  the  leg  of  the 
dividers  does  not  reach  the  end  of  the  line,  as  at  C,  it  is  evident  that  the  distance 

in   the   dividers    must   be   increased  bv 

^t •_       .»•      /?—~-  * 

rc/  y  V^T  V  A...'\  AM      -j1^  of   the  deficiency  CB' .     In  making 

N^-A^JLAJ^  either  correction,  if  the  error  is  a  con- 

Fig.  37.  siderable  one,  the  legs  of  the  instrument 

should  be  moved  by  means  of  the  head- 
joint,  but  for  a  slight  error  use  the  hair  spring,  which,  as  already  stated,  should  be 
set  before  beginning  to  space,  so  that  the  leg  may  at  once  be  moved  in  either 
direction.  Until  a  close  approximation  to  a  required  spacing  unit  is  obtained,  in- 
stead of  stepping  the  dividers  along  the  given  line,  it  is  best  to  keep  the  points  a 
little  to  one  side  of  the  line  in  order  not  to  mar  it.  In  stepping  off  the  spaces, 
care  should  be  taken  not  to  spring  the  dividers,  and  thus  change  the  distance  be- 


i 


30  SPACING  WITH  THE  DIVIDERS. 

tween  the  points  of  the  instrument  —  a  result  which  will  follow  if  the  points  are 
pushed  into  the  paper.  When  a  close  approximation  to  the  required  spacing  unit 
has  been  obtained,  the  trial  spacing  should  be  transferred  to  the  given  line ; 
but  the  paper  must  not  be  punctured  or  perceptibly  indented,  since  the  points  of 

the  dividers  are  very  likely  to  slip  back  into  the 
holes,  and  thus  to  frustrate  all  efforts  for  a  satis- 

/"  "/^"J"  ~\        factory  result.    To  minimize  error  from  failure  to 

keep  the  points  of  the  dividers  exactly  on  the  given 
line,  let  the  advancing  leg  swing  in  alternate  direc- 
tions, as  indicated  by  the  lettering  and  arrows 
(Figs.  37  and  38).  When  indicating  a  final 
•  38-  spacing,  the  paper  should  be  merely  indented,  not 

directly,  but  by  going  over  the  given  line  several  times,  each  time  with  just  enough 
pressure  to  indent  the  paper  visibly  after  the  several  repetitions. 

When  stepping  with  the  dividers,  keep  the  plane  of  its  legs  perpendicular  to  the 
paper. 

(b)  Setting  the  dividers  (or  compass)  for  a  scale  measurement.  When  setting 
the  dividers  for  a  scale  measurement,  hold  the  scale  in  the  left  hand,  with  the  face, 
as  ADC,  Fig.  39,  horizontal,  meanwhile  hold- 
ing the  dividers  so  that  the  plane  of  its  legs  !-'•' 
will  be  perpendicular  to  the  face  of  the  scale.  •<; 
Or,  place  the  scale  on  the  drawing,  with  the  it 
wrists  resting  on  the  scale,  to  keep  it  in  A) '  ,  ,7.,./.,.,.!>T,  „., ,  ,.r,  c)..y. 

place,   and   to   free   both   hands    to   manage    /r/7TTr//7T7^r7fffry'77^rr77'Lr=d 

t^(i i/ih  iiiijii// ^/ii i[ji  I,  h  L  i^/, /,/,  i ,1^,^,1,^  **(  IT 

the  dividers.     Never  hold,  with  both  hands,      <c 

the  compass  or  dividers  between  the  scale  and 

the  body  (see  the  lower  side  of  Fig.   39),  as 

the  position  is  an  awkward  one,  the  numbers 

stamped   on  the  scale  are  inverted,  and  the  ,-• 

scale   will   slip.     In    taking   a   measurement 

from  the  scale  with  the  dividers,  slight  errors  may  readily  be  detected  by  stepping 

the  dividers  along  the  scale  for  a  considerable  distance,  and  then  noting  whether 

the  total  distance  stepped  off  is  an  exact  multiple  of  the  required  distance. 

30.  Proportional  Dividers.     This  instrument  (Plate  3)   is  occasionally  very 
convenient  in  making  reduced  or  enlarged  copies  of  drawings,  photographs,  etc. 
A  required  ratio,  as  between  distances  ab  and  cd  (Plate  3),  is  obtained  by  means 
of  the  sliding  joint  A'. 

31.  India  Ink.     This  medium  — in  line  drawing  applied  with  the  ruling  and 
compass  pens  —  is  used  to  give  finish  to  a  pencil  drawing,  and  for  greater  distinct- 


INDIA  INK  —  THE  RULING  PEN. 


ness  and  durability.  It  is  also  used  in  wash  drawing,  as  described  in  Chapter  X. 
The  stick  India  ink  gives  the  best  results.  Writing  inks  are  wholly  unsuitable  for 
drawing.  The  ready  prepared  drawing  inks  are  not  here  recommended  for 
finished  drawing ;  they  do  not  flow  so  well  as  the  freshly  ground  ink,  are  not 
always  strictly  black,  and  are  likely  to  injure  the  paper  sufficiently  to  cause  fuzzy 
lines. 

(a)  To  prepare  India  ink  for  line  drawing.  Fill  the  ink  slab  (Plate  2) 
with  water  just  sufficient  to  overflow  the  ink  well.  Hold  the  stick  of  ink  vertical, 
and  with  a  moderate  pressure  give  it  a  rotary  motion  around  the  edge  of  the  ink 
well.  Continue  grinding  until  the  ink  is  absolutely  black,  but  not  thick;  this 
will  require  perhaps  five  to  ten  minutes,  according  to  the  hardness  of  the  ink  and 
the  amount  of  water  used.  As  the  grinding  proceeds,  test  the  condition  of  the 
ink  by  ruling  lines  on  paper  of  the  kind  upon  which  the  drawing  is  to  be  made.  Do 
not  judge  the  ink  before  it  is  thoroughly  dry.  The  stick  of  ink  should  be  wrapped 
as  directed  in  Art.  15,  and  wiped  perfectly  dry  after  use;  otherwise,  it  is  likely 
to  crumble.  Keep  the  liquid  ink  covered  to  prevent  thickening  and  to  keep 
out  dust.  Do  not  set  the  ink  slab  on  the  drawing  or  the  board,  but  keep  it  well 
away  from  the  work. 

32.  The  Ruling  Pen.  («)  Manipulation  of  the  pen.  To  fill  the  pen  let  it 
rest  in  the  ink  a  moment,  then  carefully  wipe  off  the  outside  of  the  blades  with  a 
rag  or  the  chamois  leather.  A  better  way,  is  to  fill  between  the  blades  with  a 
common  writing  pen  or  quill.  Always,  before  beginning  to  ink,  and  on  changing 
the  width  of  a  line,  the  pen  should  be  tried  on  the  edge  of  the  sheet,  to  see  that 
the  ink  flows  freely  and  that  the  line  is  of  a  desired  width.  Avoid  the  habit  of 
touching  the  pen  to  the  lips,  to  make  the  ink  flow ;  if  two  or  three  trials  of  the 
pen  on  the  paper,  the  finger,  or  the  drawing  board  —  where  the  pen  should  follow 
the  grain  of  the  wood  —  will  not  cause  the  ink  to  flow,  either  the  ink  is  too  thick 
or  the  pen  needs  cleaning. 

When  using  the  pen,  hold  it  perpendicular  to 
the  paper  (Fig.  40),  or  nearly  so,  with  the  tip  of  the 
forefinger  resting  on  the  head  of  the  regulating 
screw.  If  the  pen  is  inclined  in  the  direction  of  its 
motion,  it  is  difficult  to  keep  a  line  uniform  in  width, 
or  to  end  a  line  accurately  at  a  given  point.  Carry 
the  pen  from  left  to  right  steadily,  rather  slowly,  and 
without  the  slightest  rotation  about  its  axis.  To 
satisfy  this  last  condition,  the  position  of  the  hand 

relative  to  the  T-square  or  to  the  ruler  must  not  change ;  there  must  be  an  arm 
movement  from  shoulder  and  elbow,  but  no  wrist  motion.  In  drawing  a  long  line 


32 


CARE  OF  THE  RULING  PEN. 


a  slight  movement  of  the  wrist  appears  to  be  necessary,  but  this  should  not  change 
the  position  of  the  hand  relatively  to  the  ruler.  If  the  handle  of  the  pen  is  in- 
clined outward,  in  order  to  bring  the  point  into  the  line  of  contact  of  the  ruler  and 
paper,  the  ruler,  especially  if  made  of  rubber  or  steel,  is  likely  to  attract  the  ink  and 
thus  blot  the  paper ;  hence  the  blade  should  be  kept  slightly  away  from  the  lower 
edge  of  the  ruler,  unless  the  latter  is  provided  with  a  beveled  edge.  Blotting  paper 
should  always  be  at  hand  in  case  of  accident. 

When  filling  the  fen,  do  not  hold  it  over  the  drawing. 

(b)  The  care  of  the  ruling  pen.     As  the  blades  of  a  good  pen  are  highly 
tempered  and  therefore  brittle,  care  must  be  taken,  when    filling   the  pen,  not 
to  strike  the  points  against  the  ink  well ;  also,  in  setting  the  pen,  not  to  screw  the 
blades  together  too  tightly.     If  a  pen  works  badly,  the  blades  should  be  slightly 
separated  and  examined  with  a  magnifying  glass  to  see  whether  the  pen  is  dull, 
the  blades  of  unequal  length,  or  their  points  broken  off.     A  blunted  point  may  also 
be   detected  by  viewing  the  blades  endwise ;  if    it  is  dull,  a  light   spot,  due   to 
reflected  light,  will  be  seen  at  the  tip  of  the  point.     Every  student  should  learn  to 
sharpen  his  own  pen,  since  inability  to  do  this  may  prove  to  be  a  serious  handicap 
if  he  chances  in  the  future  to  be  located  at  a  point  remote  from  an  instrument  re- 
pair shop. 

(c)  To  sharpen  the  ruling  pen.     Use  a  fine  oil  stone   and    plenty    of  oil. 
With  the  blades  closed,  hold  the  pen  perpendicular  to  the  face  of  the  oil  stone, 


Fig.  4 1 . 

as  indicated  by  views  A  and  D,  Fig.  41.     Keeping  the  pen  in  a  plane  perpendicu- 
lar to  the  surface  and  parallel  to  the  long  edges  of  the  oil  stone,  carry  the  pen 


SHARPENING  THE  RULING  PEN  —  ERASURE. 


33 


Fig.  42. 


back  and  forth,  and  at  the  same  time  rock  the  pen,  as  indicated  by  positions 
B  and  C,  Fig.  41.  This  grinding  should  bring  the  blades  to  the  same  length,  and 
so  shape  the  point  of  the  pen  that,  when  seen  as  at  A,  Fig.  41,  the  outline  of  the 
point  will  appear  elliptical.  Now  grind  separately  the  point  of  each  blade  as  follows  : 
Hold  the  pen  as  shown  at  A,  Fig.  42,  making 
an  angle  of  about  10°  or  12°  with  the  surface  of 
the  stone.  Carry  the  pen  back  and  forth  as  in- 
dicated by  the  arrows,  and,  while  so  doing,  rotate 
it  about  the  axis  of  its  handle.  In  this  rotation 
the  right-hand  edge  of  the  blade,  in  passing  from 
A  to  A',  gradually  approaches  the  surface  of  the 
stone.  At  A'  the  pen  is  rotated  to  a  position 
corresponding  to  the  initial  position  (see  B}, 
and  in  the  stroke  from  B  to  B'  the  left-hand  edge 
of  the  blade  gradually  approaches  the  stone. 
The  pen  is  again  rotated  to  the  initial  posi- 
tion A,  and  the  motions  are  continued.  The 
curved  portion  of  a  cross  section  of  the  point 
should  be  approximately  elliptical.  As  the 
grinding  proceeds,  the  point  should  be  examined 
from  time  to  time  with  the  reading  glass  (Plate  2),  and  the  pen  tested  by  lines 
carefully  ruled  on  drawing  paper.  When  properly  ground,  the  blades  of  a  pen  have 
exactly  the  same  length  and  sharpness ;  if  one  blade  is  longer,  or  sharper  than  the 
other  it  will  be  difficult  to  guide  the  pen,  as  it  will  persist  in  taking  a  course  of  its 
own.  As  a  rule,  care,  patience,  and  considerable  time  are  necessary  in  order  to 
grind  a  pen  properly.  Never  grind  the  inside  of  the  blades. 

(d)  The  point  of  the  small  pen  (Plate  i)  should  be  as  sharp  as  possible  with- 
out actually  cutting  the  paper,  and  this  pen  should  be  used  only  for  fine  lines.  The 
larger  pen,  with  its  greater  ink  capacity,  is  better  adapted  for  general  work ;  the 
point  should  be  only  moderately  sharp. 

33.  Erasure,  (a)  Pencil  line.  Use  rubber  which  is  clean  and  pliable. 
When  erasing  on  thin  paper  or  tracing  cloth,  special  care  must  be  taken  not  to 
crumple  it;  hold  down  firmly  with  the  thumb  and  finger,  and  erase  between. 
For  erasure  within  a  small  space,  shave  the  rubber  to  a  point  or  wedge,  and 
use  a  card  to  protect  adjacent  lines  of  the  drawing.  Sponge  rubber  is  convenient 
for  large  areas. 

(b)  To  remove  ink  lines  from  drawing  paper.  In  office  practice,  instead  of 
a  new  drawing,  changes  in  design  are  frequently  made  on  old  drawings  by  means 
of  erasure  and  redrawing.  In  such  work,  and  in  ordinary  corrections,  removal 


34 


ERASURE  —  THE  ERASING  SHIELD. 


N 


of  blots,  and  drawing  over  an  erasure,  the  work  should  be  so  nicely  done  that  it 
will  in  nowise  deface  the  drawing  —  a  matter  requiring  knowledge,  care,  and  skill. 
Every  vestige  of  ink  should  be  removed.  Both  the  steel  eraser  and  the  sand  rubber 
(rubber  ink  eraser)  may  be  used  to  advantage,  and  the  first  step  toward 
skilful  erasure  lies  in  keeping  the  steel  eraser  very  sharp.  The  scalpel 
(Plate  2),  if  a  new  one,  should  be  reground,  and  afterwards  kept  to  a 
keen  edge  by  frequent  whetting  on  the  oil  stone.  The  form  shown  in  Fig. 
43  is  recommended.  This  edge,  but  slightly  convex,  is  best  adapted  for 
erasing  areas  ;  while  the  point,  if  kept  sharp,  is  very  satisfactory  for 
minor  erasures  and  cleaning  up  ragged  lines. 

Before  beginning  to  erase  a  line,  note  with  the  finger  whether  there 
is  a  considerable  deposit  of  ink.  If  so,  first  use  the  steel  eraser  to 
remove  as  much  of  the  ink  as  possible,  but  without  scraping  the 
paper,  and  then  apply  the  sand  rubber.  In  using  any  eraser,  the 
principal  thing  is  not  to  make  grooves  or  ruts  in  the  paper  :  hence 
the  eraser  should  be  carried  in  the  direction  of  the  line  to  be  erased, 
not  crosswise,  and  over  the  paper  for  some  distance  on  all  sides  of  the 
line,  so  that  the  paper  may  be  worn  away  uniformly.  To  the  same  end, 
in  converting  a  full  line  into  dashes,  carry  the  steel  eraser  back  and  forth 
m  ^e  direction  of  the  line,  not  crosswise.  To  prevent  ink  from  spread- 
ing, when  drawing  over  an  erasure,  the  surface  of  the  paper  should  be 
thoroughly  but  lightly  polished  with  the  burnisher  (Plate  2).  If  the  burnisher  is 
applied  too  strongly,  the  drawing  board  will  yield,  and  cause  a  rut  in  the  paper. 
To  obtain  the  best  result,  place  the  paper  on  a  hard  surface,  such  as  the  rubber 
triangle  or  a  piece  of  glass.  Excessive  gloss  due  to  burnishing  .may  be  removed 
with  the  soft  rubber  ;  but,  if  lines  are  to  be  redrawn,  the  gloss  should  not  be  re- 
moved until  the  lines  have  been  put  in. 

(c)  The  erasing  shield.  This  device  is  paper,  cardboard,  or  celluloid,  in  which 
are  cut  slits  and  holes  of  various  shapes  and  sizes.  The  shield  is  placed  over  the 
drawing,  so  that  only  the  portion  to  be  erased  will  be  exposed  to  the  rubber.  While 
shields  may  be  procured  of  dealers  in  drawing  supplies,  it  is  usually  more  convenient 
to  keep  a  sheet  of  thin  celluloid  on  hand,  and  to  cut  the  apertures  according  to 
immediate  needs. 

The  use  of  the  device  is  illustrated  in  Figs.  44,  45,  46,  and  47.  Fig.  44 
shows  a  series  of  blots  and  mistakes  at  E,  F,  .  .  .  M,  supposed  to  have  been 
made  in  a  drawing  of  the  locomotive  hand-rail  stud,  Plate  12.  In  Fig.  45  are  given 
the  forms  of  the  edges  and  of  the  apertures  in  the  erasing  shields  appropriate  in 
this  case.  Fig.  46  represents  the  drawing  after  erasure,  and  Fig.  47  the  drawing 
with  the  lines  restored.  The  edge  M'  (Fig.  45)  is  used  in  reducing  the  excess 


Fie  A.  3 


ERASURE  —  USE  OF  THE   ERASING  SHIELD. 


35 


width  of  the  lines  M  (Fig.  44).  The  full  line  lettered  E,  Figs.  44,  45,  and  46,  is 
a  mistake  in  inking,  since,  as  this  line  represents  an  invisible  edge  of  the  object,  it 
should  be  composed  of  dashes  (E,  Fig.  47).  The  line  lettered  H  (Figs.  44,  45, 


L  L^?*J          /..._¥ 

Fig.  44.  Fig.  45.  Fig.  46.  Fig.  47. 

and  46)  represents  a  visible  edge  of  the  object,  and  therefore  should  be  made  a  full 
line  as  at  H  (Fig.  47). 

(d)  To  remove  ink  lines  from  tracing  cloth.  Slip  cardboard,  glass,  or  a 
triangle  under  the  cloth,  for  a  backing,  and  then  remove  accumulations  of  ink  with 
the  steel  eraser,  which  must  not  come  in  contact  with  the  cloth.  Complete  the 
erasing  with  a  ruby  or  emerald  rubber,  using  an  erasing  shield  if  necessary.  Be- 
fore redrawing,  apply  talc  ("metal  worker's  crayon"),  and  polish  with  the  bur- 
nisher. Erasure  with  a  soft  rubber  is  easier  on  the  glazed  than  on  the  dull  surface 
of  the  cloth ;  but  in  no  case  should  the  sand  rubber  be  used,  as  it  will  quickly 
make  a  hole  in  the  cloth. 


CHAPTER    III. 

RENDERING  — CONVENTIONS  — LETTERING    AND   DIMENSIONING  —  COMMON     WORKING 

METHODS. 

34.  Rendering.     This  term  signifies  the  material  qualities  of  a  drawing,  and 
the  manner  of  its  execution.     The  material  qualities  include  the  drawing  surface  — 
as  wood,  metal,  or  paper, —  and  the  medium  employed  —  as  chalk,  graver,  pencil,  or 
ink.     The  manner  of  execution  may  rest  wholly  upon  stated,  definite  methods  —  as 
in  the  manipulation  of  the  instruments,  Chapter  II. —  or,  besides  this,  may  call  for 
individual  ingenuity,  judgment,  or  taste. 

35.  Precision  and  Speed.     The   degree   of    accuracy  with   which   a   drawing 
should  be  rendered  depends  upon  the  purpose  it  is  to   serve.     For  example,  the 
plotting  of  surveys  and  the  graphical  solution  of  engineering  problems  often  require 
the  greatest  possible  accuracy,  to  secure  which  it  may  be  necessary  to  use  a  high- 
power  reading  glass.     Working  sketches  and  architectural  sketch  rendering  are 
examples  of  the  opposite  extreme  or  free  treatment ;  here  the  principal  considera- 
tion is  speed.     The  greater  part  of  the  practical  requirement  in  drawing,  however, 
lies  between  these  two  extremes,  and  includes  both  accuracy  and  speed. 

At  the  outset,  whatever  the  character  of  his  prospective  work  in  drawing,  the 
student  should  learn  to  draw  accurately.  As  he  progresses,  he  should  learn  to 
adapt  himself  to  varied  requirements,  and  should  acquire  the  judgment  necessary 
to  work  to  the  best  advantage. 

Generally  speaking,  accuracy  of  rendering  implies  diminished  speed.  It  does 
not  follow,  however,  that  in  order  to  obtain  accuracy  it  is  necessary  to  work  slowly. 
From  the  very  start  there  should  be  a  sustained  effort  to  work  accurately  and 
rapidly ;  but  fussiness  must  not  be  mistaken  for  the  care  necessary  to  secure 
accuracy,  nor  mere  bustle  for  speed.  Speed  depends  upon  quick  judgment  and 
right  methods  rather  than  upon  quickness  of  hand. 

36.  Refinements  in  Observation  and  Manipulation.     The  following  methods 
properly  supplement  the  methods  considered  in  Chapter  II.,  when  extreme  accuracy 
is  required. 

(a)  The  line  of  sight  is  an  imaginary  straight  line  drawn  from  the  eye  to  any 
observed  point.  It  is  important  that  the  line  of  sight  shall  be  perpendicular  to 
each  observed  portion  of  the  drawing  ;  thus,  in  viewing  the  drawing  paper  in  the 

(36) 


REFINEMENTS  IN  OBSERVATION  AND  MANIPULATION.  37 

vicinity  of  B,  Fig.  48,  the  line  of  sight,  AB,  should  be  perpendicular  to  the  paper. 
This  condition  will  be  met  best  if  the  student  stands,  when  drawing,  so  that  he  may 
easily  move  about 
as  necessary  to 
bring  the  line  of 
sight  to  the  posi- 
tion indicated.  A 
block  to  incline  the 
drawing  board  is 
convenient. 

(^)  When  rul- 
ing lines,  the 
draftsman's  head 
should  move  with 
the  ruling  point. 
If  the  head  remains 
in  a  fixed  position 
and  only  the  eye 
follows  the  ruling 

point,  it  is  evident  ^. 

Fig.  48. 
that,  as  the  point 

moves  away  from  the  eye,  the  angle  which  the  line  of  sight  makes  with  the  paper 
constantly  decreases,  and,  consequently,  the  chance  of  error  increases.  Also,  in 
ruling,  the  eye  should  see  the  line  of  contact  of  the  ruler  and  paper ;  hence  the 
line 'of  sight,  AD,  cannot  be  exactly  perpendicular  to  the  paper,  but  the  angle 
BAD  (Fig.  48)  should  be  as  small  as  possible. 

In  the  case  of  a  long  line,  the  ruling  should  be  done  from  a  standing  position 
(Fig.  48).  The  draftsman  should  stand  facing,  and  with  the  left  side  of  the  body 
turned  slightly  toward,  the  drawing.  Leaning  over  the  drawing,  the  line  of  sight, 
A  C,  should  be  directed  slightly  forward  and  inward  from  the  perpendicular  AB  — 
forward,  in  order  to  see  in  advance  of  the  moving  point,  D,  and  inward,  to  see  dis- 
tinctly the  line  of  contact  of  the  ruler  and  the  paper.  Standing  as  described,  in 
drawing  a  line  the  draftsman  may  walk  forward,  whereas,  if  he  stands  with  the  right- 
hand  side  of  the  body  turned  toward  the  work,  he  is  obliged  to  walk  backward. 

(c)  In  laying  off  a  measurement  from  tJie  scale,  the  line  of  sight  must  be 
as  nearly  perpendicular  as  possible  to  the  edge  of  the  scale  at  each  of  the  two 
graduations  which  determine  the  measurement ;  that  is,  in  pricking  off  a  gradua- 
tion, as  C,  Fig.  49,  the  angle  BAC  (or  BAD)  between  the  perpendicular,  AB,  to 
the  edge  of  the  scale,  and  the  line  of  sight,  A  C,  should  be  no  greater  than  is  neces- 
sary to  bring  into  view  the  point  of  the  pricker,  or  pencil. 


REFINEMENTS    IN    OBSERVATION    AND    MANIPULATION. 


(d]     Precision  in  noting  line  intersections.     In  precise  rendering  it  is    not 
sufficient,  when  noting  an  intersection,  merely  to  glance  at  the  point,  but  it  must  be 

closely  scrutinized  in  order  that  the  point  of  the 
pricker  may  be  placed  at  the  intersection  of  the 
imaginary  center  lines  of  the  lines  of  the  draw- 
ing. To  illustrate,  let  the  black  lines,  B,  Figs. 
50  and  5  i,  represent  an  enlargement  of  the  lines 
ab  and  cd,  A,  Figs.  50  and  51,  and  the  white 
lines  (B}  represent  the  imaginary  center  lines  of 
lines  ab  and  cd.  The  intersection  of  the  white 
lines  represents  the  exact  point  at  which  the 
point  of  the  pricker  must  be  placed  when  noting 
the  intersection,  e,  of  the  lines  ab  and  cd. 

In  defining  a  tangent  point,  as  g,  Fig.   52, 


Fig.  49. 


the  position  of  the  point  of  the  pricker  should  correspond  to  the  intersection  of 
the  vertical  and  horizontal  white  lines  in  B. 

(e)     Precision  in  laying  off  scale  measurements.     The  point   of  the  pricker 


Fig.  50.  Fig.  51. 

must  coincide  exactly  with  the  intersection  of  the  center  line  of  the  graduation  and 
the  edge  of  the  scale.  (See  B,  Fig.  53,  where  the  black  areas  a',  d',  .  .  ./'  rep- 
resent enlargements  of  the  graduations  a,  b,  .  .  .  f  (A).) 

(/)     Precision  in  spacing  witJi  the  dividers.     It  is  not  sufficient  that  the  points 
of  the  dividers  fall  somewhere  near  a  given  line,  or  even  somewhere  on  this  line, 


Fig-  52.  Fig.  53. 

but  they  must  be  placed  exactly  on  the  imaginary  center  line  of  the  given  line, 
using  a  reading  glass  (Plate  2),  if  necessary.     To  illustrate  the  importance  of  this, 


CONVENTIONS. 


39 


let  it  be  supposed  that  the  points  of  the  dividers  fall  on  opposite  sides  of  the  given 
line,  as  at  the  intersection  of  the  white  lines  with  the  edges  of  the  black  area  in 
C  and  F,  Fig,  54.  It  is  evident  that  the  distance  in  the  dividers  will  be  laid  off  in 
a  zigzag  line,  and  that,  if  the 
points  of  the  dividers  fall  several 
times  on  one  edge  of  the  given 
line,  then  several  times  on  its 


Fig.  54- 


opposite  edge,  next  on  its  imag- 
inary center  line,  and  so  forth,  a 
very  slight  error  will  occur  each  time  the  dividers  is  advanced.  This  local  error, 
however  trifling,  will  be  multiplied  in  stepping  the  required  distance,  and  may 
result  in  a  perceptible  accumulated  error. 

(g)  Precision  in  drawing  circles.  A  compass  setting  taken  from  the  scale 
must  be  tested  by  drawing  a  trial  circle  and  scaling  its  diameter. 

In  the  case  of  a  large  number  of  equal  circles  the  diameter  must  be  carefully 
tested  from  time  to  time,  with  the  scale,  to  see  if  the  resharpening  of  the  compass 
lead  has  changed  the  radius. 

37.  Conventions.  (#)  Line  conventions  commonly  used  in  inking  mechan- 
ical drawings  are  given  in  Fig.  55.  The  cut  shows  the  true  width  of  line,  length 


For 


Full  line 


problems   | 
and  other  •{   Dash  line  .     .     .     . 
fine-line    j 
work       [_  Dash  and  dot  line  . 

Visible  lines  .     .     . 
Shade  lines    .     .     . 

For  Invisible  lines    .     . 

working  ^ 


drawings 


Center  lines  .  . 
Extension  lines  . 
Dimension  lines 


Fig-  55- 


of  dash,  and  space  between  dashes.  The  student  should  become  familiar  with 
the  relative  line  widths,  lengths  of  dashes,  and  spaces  by  frequently  comparing  the 
lines  in  the  figure.  Greater  distinctions  may  be  obtained  by  using  colored  inks, 
which  also  saves  time  since  lines  in  color  are  usually  made  full. 

The  conventions  shown  in  Plate  4  are  used  more  or  less  in  practice,  and,  as  an 
exercise  in  rendering,  afford  excellent  training. 

(6)  Breaks.  When  only  a  portion  of  an  object  is  represented,  this  fact  may 
be  indicated  by  an  irregular  line,  as,  for  example,  at  F,  Fig.  A  (Plate  4),  and  the 


4O  CONVENTIONS. 

drawing  is  said  to  be  "broken  off."  To  economize  space,  an  object  may  be  repre- 
sented as  broken  and  brought  together,  as  in  the  first  and  last  examples,  Fig.  A.  A 
break  in  a  metal  piece  rectangular  in  section  may  be  indicated  according  to  E  and 
E' ;  a  break  in  a  wooden  piece,  according  to  either  of  the  two  styles  of  treatment 
//and  H' .  A  cylindrical  piece  may  be  broken  as  shown  in  Fig.  B,  and  the  surface 
of  the  break  cross  hatched  or  not,  according  to  personal  preference  or  the  custom 
of  the  office. 

(c)  Graining.     A  wooden  piece  seen  lengthwise  may  be  grained  as  shown  in 
F,  Fig.  A,  an  end  view  as  shown  at  F' . 

(d)  Section  lining  or  cross  hatching.     The  conventions,  Fig.  ^indicate  ma- 
terial as  follows :  — 

J,    Cast  Iron.  L,    Wrought  Iron.  N,  Composition. 

K,  Cast  Steel.  M,  Wrought  Steel.  O,  Babbitt. 

The  series  P,  Q,  .  .  .  U,  is  the  same  as  the  series  J,  K,  ...  O,  except  that  the 
areas  are  larger,  which  requires  that  the  lines  of  the  cross  hatching  shall  be  coarser 
and  more  openly  spaced. 

(e)  Conventional  line  shading  (Fig.  D),  is  used  in  drawings  for  cuts  of  me- 
chanical objects  and,  to  a  very  limited  extent,  in  engineering  drawing  (see  c,  Art. 
66).     The  number  of  lines,  and  their  spacing  and  respective  widths  in  a  piece  of 
shading,  depend  upon  the  size  of  the  shaded  area  and  the  effect  desired.     For 
example,  the  effect  of  a  highly  polished  surface  might  be  suggested  by  means  of  a 
shading  lighter  than  that  used  on  other  surfaces. 

38.  Rendering  of  the  Conventions,  Plate  4.  (a)  Breaks  and  graining. 
These  conventions  (Figs.  A  and  B]  should  be  rendered  with  a  writing  pen,  of  a 
grade  suited  to  the  character  and  size  of  the  drawing,  wholly  freehand,  and  in  flexible 
line.  The  outline  of  the  break,  Fig.  B,  should  be  of  uniform  width,  curved  through- 
out its  entire  length,  and  be  drawn  tangent  to  the  contour  elements  of  the  cylinder. 
In  general,  these  conventions  should  be  rendered  with  regard  to  their  general 
effect ;  but  in  first  attempts  the  plate  should  be  closely  copied. 

(b)  Cross  hatching  (Fig.  C}.  The  lines  of  the  several  cross  hatchings  should 
be  drawn  at  45°  with  the  horizontal,  except  in  conventions  O  and  U,  where  the  lines 
are  drawn  at  60°.  Place  the  proper  triangle  against  the  T-square,  and  space  the 
lines  wholly  by  eye,  or  by  touch  —  that  is,  by  sensing  the  amount  the  triangle 
should  be  moved  to  obtain  the  required  spacing. 

Conventions  L  (R)  and  M  (S)  should  be  treated  in  the  following  manner : 
Let  Rf  represent  the  section  lining  at  the  upper  left-hand  corner  of  example  R. 
Set  the  pen  for  the  narrow  lines  in  R,  and,  keeping  the  same  width  of  line,  repre- 
sent the  wider  lines  in  R  by  double  lines,  as  at  D  and  E  (R'}.  Cross  hatch  the 
whole  surface,  and  then  fill  in  the  narrower  spaces  to  make  the  wide  lines.  Make 


Plate  4 

CStudy   Plate  3) 


The  dimensions  and  reference  letters  should  not  appear  on  the  students  drawing 


CONVENTIONS  —  LETTERING  .  43 

the  spaces,  as  A,  B,  and  C  (ft'),  between  the  narrow  lines  and  the  edges  of  the 
wide  lines  equal  in  width. 

Some  draftsmen  insist  that  if  a  break  is  cross  hatched  (see  Fig.  B),  it  should 
be  done  freehand. 

The  instrument  known  as  a  section  liner  may  be  convenient,  or  perhaps  neces- 
sary, in  making  fine  drawings  and  cuts ;  but  this  instrument  must  not  be  used  in 
the  exercises  here  given. 

(c)  Conventional  line  sJiading  (Fig.  D].  The  spacing  and  widths  of  line 
must  be  determined  wholly  by  eye.  A  preliminary  penciling  of  a  narrow  strip 
of  the  shading  (as  shown  below  V,  V ,  and  V",  Fig.  Z>),  to  establish  the  num- 
ber of  lines,  spacing,  and  line  widths,  should  be  indicated ;  but,  with  this  exception, 
the  shading  must  be  done  directly  with  the  ruling  pen.  Begin  at  the  left-hand 
border  of  a  vertical  piece  and  at  the  upper  border  of  a  horizontal  piece. 

In  the  case  of  a  cylinder  first  set  the  pen  for  a  very  narrow  line,  and,  while 
changing  the  spacing,  retain  the  same  width  of  line  until  the  wider  lines  at  the 
right-hand  third  of  the  cylinder  are  reached.  Then,  besides  changing  the  spacing, 
gradually  increase  the  width  of  line  by  changing  the  setting  of  the  pen.  The 
widest  lines  of  the  shading  may  need  to  be  built  up  by  going  over  each  several 
times,  in  which  case  let  the  lines  dry  frequently  in  order  to  avoid  blots.  When  all  of 
the  shading  has  been  thus  laid  in,  the  narrower  lines  may  be  retouched,  if  necessary, 
and  the  spacing  and  line  widths  of  the  right-hand  third  of  the  cylinder  corrected. 

Excellent  examples  of  line  shadings  in  great  variety  may  be  found  in  catalogues 
of  machinery,  etc.,  illustrated  with  fine  woodcuts.  In  first  attempts,  an  example 
should  be  closely  copied,  not  line  by  line,  but  for  its  general  effect. 

39.  Lettering.  In  connection  with  the  study  of  mechanical  drawing  it  is 
important  to  have  extended  practice  in  lettering  and  dimensioning  (Art.  42). 

(a)  Styles  and  sizes  of  letters.  In  Plate  5  are  given  vertical  and  inclined 
Gothic  letters  and  numerals  in  two  sizes  and  widths  of  line,  which  should  be  used 
in  rendering  data  and  dimensions  on  the  practice  drawings  that  follow.  These 
styles  should  also  be  used  for  titles,  but  the  letters  must  be  larger. 

There  should  be  lettered  on  the  margin  of  each  finished  practice  drawing  the 
word  "Plate"  the  number  of  the  plate,  the  student's  name,  and  the  date  on  which 
the  drawing  is  completed.  The  required  heights  of  the  letters,  for  two  sizes  of 
border  line,  are  given  in  Fig.  56. 

The  general  effect  of  the  lettering  and  dimensions  of  a  drawing  should  cor- 
respond with  the  general  effect  of  the  drawing.  That  is,  if  the  drawing  is  strong 
in  appearance,  a  bold  letter  should  be  used  ;  but,  if  a  drawing  is  light  or  weak  in  its 
general  effect  —  as  in  a  geometrical  construction  —  a  lighter  letter  should  be 
selected  (compare  Figs.  A  and  C,  Plate  5). 


44 


LETTER  RENDERING. 


40.     Stroke  Letters,     (a)     Rendering.     In  office  practice  it  is  commonly  re- 
quired that  small  titles,  reference  letters,  and  dimensions  shall  be  rendered  with 


"»* 


»4- 


vf PILATE  5 

1      t  ^ 


-/£  "*  /8"  ru/ed  border-line 


-8"*  12"  ruled  border-fine 


'.  JOKTTicutL 


-£- 


DATE: 


Fig.  56. 


direct  strokes  of  the  pen,  rapidly,  and  without  the  use  of  guide  lines.  A  system 
of  stroke  letters  is  given  in  Fig.  J  (Plate  5)  :  the  arrows  show  the  direction  in 
which  the  pen  should  be  carried  ;  and  the  numerals,  the  order  in  which  the  strokes 
should  be  made. 

The  practice  drawings  here  given  must  be  lettered  and  dimensioned  according 
to  this  system,  unless  otherwise  specified.  To  acquire  proficiency,  the  student 
should  practice  daily  the  alphabets,  Plate  5,  until  he  can  make  the  letters  and  nu- 
merals with  a  fair  degree  of  speed  and  uniformity.  For  a  line  of  letters  or  nu- 
merals, one  base  or  guide  line,  only,  may  be  ruled. 

(&)  Lettering  pens.  For  rendering  dimensions  and  data  —  when  the  letters 
and  numerals  have  a  width  of  line  corresponding  to  that  of  the  letters  in  Fig.  C  or 
D,  Plate  5  —  a  No.  303  Gillott's  pen  is  recommended.  Letters  having  a  consider- 
able width  of  line  —  as  wide  as  that  in  Figs.  A  and  B  —  may  be  rendered,  according 
to  preference,  with  a  coarse  writing  pen,  a  ball-point  pen,  a  turned-point  pen,  or  a 
ruling  pen  specially  ground  for  lettering. 

(c)  Letter  rendering  with  the  ruling  pen.  A  reproduction  of  a  piece  of  rapid 
stroke  lettering  with  the  ruling  pen  is  given  in  Fig.  57.  The  cut  is  half  the 
size  of  the  original,  which  was  taken  from  a  large  number  of  office  drawings  equally 
well  lettered,  and  in  a  like  manner. 


Plate  5 


ABCDEFGH  U  KLM  NOPQRSTU  VWXYZ 
I234567890&    abcdefghijklmnopqrstuvwxyz 

Fig.  A.   ' 

ABCDErGH/JKLMNOPQRSTUVWXYZ 


Fig.  B. 

ABCDEFGHUKLJV1NOPORSTUVWXYZ 
I2345678906c    abcdefgh||klmnopqrstuvwxyz 

Fig.  C. 


aobcde/gh/Jk/mnopqrstuvwxyz 

Fig.  D. 


ABCDEFGHIJKLMNOPQRSrUVWXYZ 

I2345678908t    abcdefghijklmnopqrstuvwxyz 

Fig.  E. 


Fig.  F. 

ABCDErGHUKLMNOPQRSTUVWXYZ 

1234567890&    abcdefghijklmnopqrstuvwxyz 

Fig.  G. 

ABCDEFGHUKLMNOfJQnSTUVWXYZ 
aobcdefyhfo/mnopqrstuvwxyz 
Fig.  H. 


5*S 

W^&/*^itWM1/g? 

3VV^*      T 

Fig.  J. 


Fig.  K. 

(45) 


LETTER  RENDERING. 


47 


The  special  advantage  in  lettering  with  the  ruling  pen  is  the  increase  obtain 
able  in  the  size  of  a  letter  and  its  width  of  line.  An  inexpensive  pen,  or  one  which 
has  proved  unsatisfactory  for  ruling,  is  sufficiently  good  for  the  purpose. 

(d)      To  grind  a  ruling  pen  for  lettering.     Hold  the  pen  perpendicular  to  the 
oil  stone  and  grind  until  the  point  is  very  blunt.      Next  hold  the  pen  as  in  Fig.  42, 


r^\nJK--^B^T£r^^^  j^tr 


Hours 


Fig-  57- 


and  grind  until  the  two  blades,  taken  together,  are  conical  in  shape,  except  at  the 
point,  which  should  remain  blunt.  To  shape  the  point,  start  with  the  pen  held 
perpendicular  to  the  stone,  and  carry  its  point  in  a  circular  path,  meanwhile  con- 
stantly changing  the  direction  of  the  pen  to  all  angles  from  the  perpendicular  to 
45°  with  the  stone  —  a  movement  which  changes  the  roughly  blunted  point  to  one 
having  a  spherical  shape. 

(e)  Manipulation  ;  lettering  with  the  ruling  pen.  Hold  the  pen  at  any  angle 
between  45°  and  60°  with  the  paper,  with  the  regulating  screw  horizontal  and  the 
thumb  resting  against  the  head  of  the  screw.  Render  the  letters  according  to  J, 
Plate  5.  It  is  best  to  fill  the  pen  with  the  common  writing  pen,  or  a  quill,  as  wip- 
ing is  likely  to  absorb  too  much  ink  from  between  the  blades. 


48 


LETTER  RENDERING. 


41.  Drawn  Letters.  When  letters  and  numerals  are  gradually  built  up  or  de- 
veloped by  stages  —  as  is  necessary  for  the  most  finished  results  in  freehand  letter- 
ing —  they  are  said  to  be  drawn. 

(a)  Rendering  of  drawn  letters.  Guide  lines  must  be  ruled  as  shown  in  Figs. 
58  and  62.  All  letters  and  numerals  throughout  the  drawing  should  be  developed 


A                             4-            B     _,U 

j     .1 

*  I  a    '->  JL/I  '•'         3iE              U^PF 

gac 

.    g2    S  >jl 

-*',  / 

Fig.  58. 
A                                            B 

;"•'>. Afrtt.K  V\ -AM I-.'.-! 


Fig-  59- 


m 

!*- — . —  -    y    .  -——^. 

T^./^M  L-l  J-3 


-a- 


:=  if    i.       UKAwK    BY  A.KL 


Fig.  60. 


X 

/m 

j   r          A 

Xj    f~I  >*{ 

^ 

/m 

.••*_.,•»!  .!".    1?^=:  f  \- 

!.»KAVv'-»;  BY  A. 

~i*~ 

!••»•:«.  ij 

.  i  '.-'  '.'  .S 

Fig.  62. 


Fig.  61. 

wholly  freehand,  in  the  following  order.  (I.)  Suggest  in  pencil  (A,  Fig.  59)  the 
letters  and  numerals  —  for  their  sizes  and  position  relatively  to  the  drawing  or  its 
parts.  (II.)  Correct  the  pencil  suggestions,  for  the  spacing,  form,  and  verticality,  or 
slant,  of  the  letters  (B,  Fig.  59).  (III.)  Without  changing  the  treatment  (A  and  B\ 
ink  in  the  suggestions  throughout  the  drawing,  but  at  the  same  time  make,  if  nec- 
essary, further  corrections  in  the  form  and  verticality,  or  slant,  of  the  letters  and 
numerals  (no  figure).  (IV.)  Connect  or  pull  together  the  blocks  of  the  suggestions 


LETTER  RENDERING  —  DIMENSIONING. 


49 


(C,  Fig.  59).      (V.)  Bring  the  lines  to  the  required  width  and  complete  the  letters, 
making  all  edges  sharp  and  true  (D,  Fig.  59). 

(b)     Balancing  a  title,  or  a  line  of  letters.     When  one  or  more  lines  of  letters 
must  be  balanced  on  a  given  line,  as  XY,  Fig.  61,  proceed  as  follows :  Lay  off 


Fig.  63. 

accurately  the  heights  of  the  letters,  and  rule  the  guide  lines  (Fig.  60)  on  a  slip 
of  paper,  but  without  regard  to  their  position.  Suggest  each  line  of  the  title  (Fig. 
60).  Find  the  middle  point,  as  m,  of  each  line  of  letters ;  fit  the  middle  point,  m, 
on  the  center  line,  XY,  of  the  final  title  (Fig.  61)  ;  mark  off  the  letter  widths,  and 
develop  the  letters  by  stages  as  indicated  in  paragraph  a. 

42.  Dimensioning.  This  term  signifies  the  giving  of  measurements  on  draw- 
ings (Fig.  63),  and  includes  the  rendering  of  the  numerals,  their  arrangement  on 
the  drawing,  and  the  selection  of  their  size  and  style. 


DIMENSIONING  —  PRELIMINARIES  TO  DRAWING. 


A  dimension  line  is  the  broken  line  connecting  the  arrow  heads  which  indicate 
the  points  of  a  measurement.  Extension  lines  (see  the  vertical  lines  composed  of 
short  dashes,  Fig.  63)  are  used,  in  case  of  interference  or  confusion,  to  carry  points 
of  measurement  to  another  part  of  the  drawing.  Line  widths  and  length  of  dashes 
for  both  dimension  and  extension  lines  are  given  in  Fig.  5  5 . 

Numerals  of  a  size  suitable  for  dimensioning  average-sized  drawings,  and  for 
the  study  plates,  together  with  the  proper  form  of  arrow  heads,  are  given  in  Fig. 
K,  Plate  5.  The  sign  '  means  feet,  and  the  sign  "  means  inches:  thus  io'-6-|-" 
is  read  ten  feet,  six  and  one-half  inches.  Inclined  signs  are  always  used  by  printers, 
but  in  dimensioning  a  drawing  vertical  signs  should  be  used  with  vertical  numerals, 
and  inclined  signs  with  inclined  numerals.  The  quantities  feet  and  inches  must 
always  be  separated  by  a  dash  (Fig.  K,  Plate  5).  The  numerator  and  the  de- 
nominator of  a  fraction  should  each  be  balanced  on  the  center  line  of  the  fraction 
taken  as  a  whole  (see  the  T9g,  Fig.  K,  Plate  5). 

43.  Preliminaries  to  Drawing.  A  finished  drawing  is  usually  circumscribed 
by  a  ruled  border  line,  EEEE,  Fig.  64,  the  dimensions  of  which  may  be  given, 

or  which  must  be 
determined  from  the 
size  and  arrangement 
of  the  drawings  on 
the  sheet.  Outside 
of  the  ruled  border 
a  margin,  DDDD, 
Fig.  64,  should  be 
laid  off,  and  lines, 
CCCC,  drawn  for  the 
boundary  of  the  fin- 
ished plate  when 
trimmed.  Therefore, 
to  ascertain  the  size 
of  the  paper  required 
for  a  drawing,  add  to 
the  dimensions  of  the 


A 

Fig.  64. 


ruled  border  line  twice  the  width  of  the  margin,  together  with  an  allowance  of 
extra  paper  for  thumb-tack  holes,  which  must  fall  outside  the  trimmed  edge. 

Never  begin  work  on  paper  larger  than  the  drawing  board  ;  if  the  paper  pro- 
jects beyond  the  board,  immediately  trim  the  edges  so  that  all  shall  lie  at  least  ^  inch 
inside  the  edges  of  the  board.  As  the  T-square  is  likely  to  work  less  accurately 
near  the  lower  edge  of  the  board,  the  paper,  when  smaller  than  the  board,  should  be 


PRELIMINARIES  TO  DRAWING. 


JTl 


Avoid 


placed  well  above  its  lower  edge  (Fig.  66)  .     Smooth  the  paper  flat,  place  it  squarely 
on  the  board,  and  start  the  thumb  tacks  at  right  angles  to  the  board  (A,  Fig.  65), 

so  that,  when  the  tack  is  pressed  in,  the  head 
will  bear  evenly  on  the  paper  (B,  Fig.  65). 
Never  use  the  T-square  to  drive  in  thumb 
tacks. 

Provide  a  piece  of  clean  cloth  or  paper 
with  which  to  protect  the  drawing  ;  when 
not  at  work  on  the  drawing,  keep  it  covered. 
Also,  when  working  on  a  large  or  carefully 
executed  drawing,  cover  all  parts  not  re- 
ceiving immediate  attention. 

(a)  To  lay  out  a  ruled  border  line. 
Take,  for  example,  a  plate  which  shall  have 
an  8  in.  x  12  in.  ruled  border  line  and  a 

margin  i  in.  wide.  Let  A,  A,  Fig.  66,  represent  the  edges  of  the  paper  cut  for  the 
drawing,  according  to  the  preceding  paragraph.  With  the  aid  of  the  T-square,  place 
the  edges  of  the  paper  approximately  parallel  to  the  edges  of  the  drawing  board. 
With  the  T-square  and 
triangle,  draw  horizon- 
tal and  vertical  lines, 

B,  B,  -£-  in.  or  more  from 
the  edge  of  the  paper,  to 
allow  for  the  trimming, 
and  thumb  tack  holes. 
Perpendicular    to    the 
lines  B,  B,  lay  off  i  in., 
the  given  width  of  the 
margin.       Draw    lines, 

C,  C,  of  indefinite 
lengths,    and    lay    off 
the  dimensions  of  the 
border  line.     Complete 
the  border  line  with  the 


Fig.  66. 


T-square  and  triangle.  Lay  off  the  widths  of  the  right-hand  and  lower  margins, 
and  draw  the  remaining  trimming  lines. 

When  a  strictly  accurate  border  is  necessary,  it  should  be  laid  out  by  geomet- 
rical construction  (see  Problem  4,  Chapter  V.). 

(b)     Trimming.     A  very  sharp  knife  or  scissors  should  be  used  for  trimming 


52  WORKING  METHODS. 

drawings.  When  trimmed  on  a  board,  the  drawing  should  be  so  placed  that  the 
knife  will  be  drawn  across  rather  than  with  the  grain  of  the  wood  ;  otherwise  the 
knife  is  liable  to  follow  the  grain,  and  prevent  a  straight  cut.  The  best  cutting  sur- 
face is  thick,  smooth  cardboard  laid  on  the  drawing  board.  The  regular  drawing 
board  and  T-square  should  not  be  used  in  trimming  drawings,  but  separate 
ones  should  be  kept  for  this  purpose.  If,  as  a  last  resort,  the  regular  drawing 
board  and  T-square  are  used,  the  cutting  should  be  done  on  the  back  of  the  board 
and  along  the  lower  edge  of  the  T-square. 

44.  Common  Working  Methods,  (a)  Drawing  by  stages.  For  convenience 
and  to  emphasize  methodical  procedure,  the  rendering  of  a  drawing  may  be  divided 
into  stages,  as,  for  example:  (I.)  the  constructive  stage,  represented  by  the  laying 
out  of  a  drawing  and  all  instrumental  penciling ;  and  (II.)  the  finishing  stage,  repre- 
sented by  the  inking,  or  by  the  final  lining  in  of  a  finished  pencil  drawing. 
Furthermore,  a  general  stage  may  include  any  number  of  local  stages,  as  described 
in  connection  with  Figs.  69-73. 

The  general  stages  of  a  drawing  are  illustrated  in  Fig.  67,  which  represents  an 
end  of  a  marine  engine  connecting  rod.  The  upper  half  of  the  cut  shows  the  con- 


Fig.  67. 

structive  stage ;  the  lower  half  shows  the  finishing  stage,  with  the  lines  of  the 
constructive  stage  left  in  for  the  purpose  of  comparison. 

(£)      The    constructive   stage ;   penciling.      The    penciling  should   invariably 
represent  the  degree  of  accuracy  required  in  the  finished  drawing ;  that  is,  essen- 


\ 


WORKING  METHODS.  53 

tials  must  never  be  slighted  with  the  idea  that  they  may  be  corrected  when  the 
drawing  is  lined  in,  or  inked.  In  the  constructive  stage  all  lines  should  be  full,  of 
uniform  width,  light  but  firm,  very  narrow,  and  made  with  as  hard  a  pencil  as  the 
paper  used  will  permit.  Dash  lines  should  not  be  used  in  this  stage,  as  they  can- 
not be  made  so  rapidly  as  full  lines  ;  furthermore,  as  suggested  in  Fig.  68,  desired 

intersections,  as  at  A,  B,  and  C,  are 
N^'*'  likely  to  be  merely  open  spaces. 

\  Lines  upon  which  measurements 

are  to  be   laid  off,  as  CD,  Fig.  67, 
must  be  drawn  long  enough  to  insure 
^''  \  the   laying  off   of   the   measurement 

xx^x  \  without    patching    out   a   line.     The 

~x"^ -^—    same  is  the  case  with  lines  required  to 

x       be  intersected  by  subsequent  lines,  as 
AE,   AB,   and   the    other    produced 

lines  in  Fig.  67.  To  save  time  and  to  avoid  patching,  circles,  as  at  FGH,  which 
are  more  or  less  broken  up  in  the  finished  drawing,  should  be  drawn  complete  in 
the  penciling. 

There  should  be  little  or  no  erasure  when  a  drawing  is  in  progress,  and  it 
should  not  be  cleaned  until  finished,  as  the  paper  soils  more  quickly  after  the  rub- 
ber has  been  used. 

(c)  The  finishing  stage  of  a  pencil  drawing  {finished  rendering].     The  use  of 
line  conventions  should  be  confined  to  this  stage  of  the  drawing,  and  rendered  in 
connection  with  the  lining  in.     Use  a  rather  soft  pencil  (F  to  3H)  and  emphasize 
all  lines  strongly.     Dashes  should  be  drawn  with  a  deliberate  stroke,  not  merely 
touched  in,  and  the  ends  of  each  dash  should  be  clearly  defined.     All  dashes  of  the 
same  convention  should  be  equal  in  length,  and  the  spaces  between  the  dashes  made 
equal.     The  lines  of  the  constructive  stage  need  not  be  erased  between  the  dashes, 
as  they  become  inconspicuous  if  the  dashes  are   sufficiently  emphasized.     In  a 
carefully  rendered  drawing,  dimension  and  extension  lines  (Art.  42)  should  first  be 
lightly  ruled,  in  full  line,  in  connection  with  the  suggestion  of  the  numerals,  and 
the  dashes  should  be  put  in  later  along  with  other  conventions. 

(d)  The  finishing  stage  of  an  inked  drawing  {finished  rendering).     This 
stage  includes,  besides  inking,  the  rendering  of  dimensions  and  lettering  (Arts.  39 
and  42)  —  which    should  not  precede   the  inking  —  together  with  any   penciling 
connected  therewith.     All  line  conventions  should  be  rendered   directly  in  ink ; 
that  is,  without  a  preliminary  penciling  of  the  convention.     Make  all  lines  perfectly 
smooth,  and,  except  in  the  case  of  curved  shade  lines,  keep  all  lines  of  the  same 
class  uniform  in  width.     Each  dash  should  have  the  same  width  throughout,  and 
the  ends  should  be  made  square  or  perpendicular  to  the  direction  of  the  dash. 


54 


WORKING  METHODS. 


Every  line  should  be  carried  accurately  to  its  destination,  neither  falling  short  of 
nor  extending  beyond  it ;  special  attention  should  be  given  to  the  rendering  of  cor- 
ners, that  all  may  be  perfect. 

(e)  Inking  by  stages.  To  save  time  and  also  to  minimize  the  chance  of 
smearing  wet  ink,  similar  operations  should  be  grouped,  as  indicated  in  the  follow- 
ing model,  which  shows  the  steps  actually  taken  in  inking  and  dimensioning  the 
original  drawing  for  Fig.  69. 

Beginning  at  the  upper  left-hand  corner  of  the  drawing  and  —  to  avoid  wet  ink 
—  working  downward  and  from  left  to  right:  (I.)  Ink  all  circles  and  arcs  of  the 


Fig.  70. 


Fig.  71. 


Fig.  72. 


Fig-  73- 


same  radius,  then  all  remaining  circles  and  arcs  (Fig.  70).  (II.)  Ink  the  vertical 
lines  (Fig.  71).  (III.)  Put  in  all  the  horizontals  and  other  remaining  full  lines 
(Fig.  72).  (IV.)  Draw  the  dash  lines  (Fig.  73).  (V.)  Render  the  shade  lines 
(Fig- 73)-  (VI.)  Render  the  dimensions  (Fig.  73).  (VII.)  Draw  the  screw-thread 
convention  ;  indicate  the  breaks ;  and  cross  hatch  the  section  (Fig.  69) . 

(/)      The  inking  of  convergent  lines.     To  prevent  lines  from  running  together 


Fig.  74- 

near  their  point  of  convergence,  or  intersection  (A,  B,  and  C,  Fig.  74),  let  each 
line  dry  before  inking  another,  and  carry  the  pen  away  from  the  point  of  conver- 
gence rather  than  towards  it ;  or  terminate  the  interior  lines  (D  and  E,  Fig.  74)  at 
an  arc  described,  in  pencil,  from  the  point  of  convergence  taken  as  center. 


WORKING   METHODS. 


55 


(£•)  Shade  lines.  When  shade  lines  (Art.  58)  are  shown  on  a  drawing,  the 
extra  width  of  line,  whenever  practicable,  should  be  added  to  the  outer  edges  of 
straight  and  curved  lines  so  as  not  to  encroach  upon  the  sur- 
face area  bounded  by  the  lines.  In  the  case  of  a  circle  or  a 
circular  arc,  the  shade  line  should  be  placed  by  shifting  the 
center.  Thus,  for  example,  in  drawing  shade  lines  mhk  and 
egf*  Fig.  75,  the  center  was  shifted  from  a  to  r,  a  point  in 
the  line  dg  drawn  at  45°  to  the  horizontal,  the  distance  ac 
being  determined  by  eye.  It  will  be  observed  that  the  shade 
lines,  as  thus  drawn,  do  not  encroach  on  the  surface  included 
between  the  two  circles.  Likewise  the  shade  line  stnv,  added 
to  the  outer  edge  of  line  st,  does  not  encroach  upon  the  sur- 
face, qrst,  of  the  ring. 


1 

1 

Fig-  75- 


(//)  Testing.  The  accuracy  of  a  drawing  should  be  frequently  verified  by  check- 
ing or  testing  ;  in  office  practice,  this  is  the  only  safeguard  against  costly  mistakes. 

45.  Solution  of  Geometrical  Problems  by  Practical  Working  Methods.  It  has 
already  been  stated  (Art.  23)  that  in  practical  drawing  parallels,  perpendiculars, 
and  angles  of  15°,  30°,  45°,  60°,  and  75°  are  obtained  by  means  of  the  T-square 
and  triangles,  or  by  the  triangles  alone.  There  are  many  other  cases,  however, 
where  exact  geometrical  construction  (see  Chapter  V.),  is  unnecessarily  laborious, 
and  where  accurate  results  may  be  obtained  by  shorter  methods,  some  of  which  are 
given  below.  Apart  from  the  value  of  the  methods  as  such,  it  is  intended  that 
they  shall  suggest  to  the  student  further  possibilities  in  the  use  of  the  triangles 
and  compass.  Speed,  without  the  sacrifice  of  accuracy,  often  depends  on  a  ready 
application  of  some  particular  instrumental  method. 

(a)  To  draw  a  line  perpendicular  to  a  given  line 
at  its  middle  point.  Let  A B  be  the  given  line.  From 
the  ends,  A  and  B,  of  the  line,  draw  lines  A  C  and  BC, 
making  equal  angles  with  AB.  (Make  these  equal 
angles  either  30°,  45°,  or  60°;  if  the  given  line  is 
neither  horizontal  nor  vertical,  proceed  according  to  D  and  E,  Fig.  23.)  From 
the  intersection  C,  draw  the  required  line  CD  perpendicular  to  AB  (see  B, 
Fig.  23). 

(b}  To  draw  a  circular  arc  through  three  given 
points.  Let  A,  B,  and  C  be  the  given  points.  Draw 
AB  and  BC.  Draw  DO  perpendicular  to  AB  at  its 
middle  point  (see  a}.  Draw  EO  perpendicular  to  BC 
at  its  middle  point.  The  intersection,  O,  is  the  center 
of  the  required  arc. 


WORKING  METHODS. 


f 


(c)  To  draw  a  tangent  to  a  circular  arc  at  a  given 
point  on  the  arc.  Let  C  be  the  given  point  on  the  arc, 
center  O.  Draw  the  radius  OC ;  at  C  draw  the  re- 
quired tangent  AB  perpendicular  to  OC  (B,  Fig.  23). 

(d}      To  find  the  point   of  tangency   of  a  given 

straight  line  and  circular  arc.  Let  AB  be  the  tangent  to  the  arc,  center  O.  From 
O  draw  OC  perpendicular  to  AB  (B,  Fig.  23) ;  the  intersection,  C,  is  the  required 
point  of  tangency. 

(e)  To  find  the  point  of  tangency  of  two  given 
circular  arcs.  Let  A  and  B  be  the  centers  of  the 
given  arcs.  Draw  AB ;  the  intersection,  C,  is  the  re- 
quired point  of  tangency. 

(/)  To  draw  an  arc  of  a  given  radius  tangent  to  two  given  lines  at  right 
angles.  Let  AB  and  BC  be  the  given  lines.  Set  the  compasses  to  the  given 
radius;  then,  with  B  as  center,  intersect  AB  and  BC  A 
at  D  and  E.  With  the  same  radius,  centers  D  and 
E,  draw  arcs  intersecting  at  O,  the  center  of  the 
required  arc.  Points  D  and  E  are  the  points  of 
tangency. 

(g)  To  draw  a  line  parallel  to  a  given  line  at  a  given  distance  from  it.  Let 
AB  be  the  given  line.  Set  the  compasses  to  a  radius  equal  to  the  given  dis- 
tance, then,  with  any  point  on  AB,  as  C,  for  a  center, 
draw  an  arc.  Draw,  tangent  (by  eye)  to  the  arc,  the 
required  line  DE  parallel  to  AB  (A,  Fig.  23).  Note. 
There  are  two  solutions  possible,  one  on  each  side  of 
the  given  line. 

(//)  To  draw  a  circular  arc  parallel  to  a  given  circular  arc,  and  at  a  given 
distance  from  it.  Let  AB,  center  O,  be  the  given  arc.  Draw  any  radius  OC. 
Make  CD  equal  to  the  given  distance.  With  radius  A/ 

DO,   center    O,   draw   the    required    arc   DE.      Note.  \  *•<> 

There  are  two  solutions  possible,  one  on  each  side  of 

the  given  arc.  6\ 

(i)  To  draw  an  arc  of  a  given  radius  tangent  to  two  given  intersecting^, 
straight  lines.  Let  AB  and  BC  be  the  given  lines.  Draw  DE  parallel  to  AB 
at  a  distance  equal  to  the  given  radius  (see  g).  Draw 
FG  parallel  to  BC  at  a  distance  equal  to  the  given 
radius.  The  intersection,  O,  is  the  center  of  the  re- 
quired arc  ;  the  points  of  tangency  may  be  found  accord- 
ing to  d.  Note.  There  are  four  solutions  possible. 


WORKING  METHODS. 


57 


(/)  To  draw  an  arc  of  a  given  radius  tangent  to  a 
given  circular  arc  and  to  a  given  straight  line.  Let  AB 
be  the  given  circular  arc,  and  AC  the  given  straight 
line.  Draw  arc  DE  parallel  to  arc  AB  at  a  distance 
equal  to  the  given  radius  (see  ti).  Draw  line  FG  parallel 
to  line  A  Cat  a  distance  equal  to  the  given  radius  (see  g).  The  intersection,  O, 
is  the  centre  of  the  required  arc ;  the  points  of  tangency  may  be  found  according 
to  d  and  e.  Note.  There  may  be  four  solutions  possible. 

(k]  To  draw  an  arc  of  a  given  radius  tangent  to 
two  given  circular  arcs.  Let  AB  and  BC  be  the  given 
circular  arcs.  Draw  arc  EF  parallel  to  arc  AB  at  a  dis- 
tance equal  to  the  given  radius  (see  Ji).  Draw  arc  GH 
parallel  to  arc  BC  at  a  distance  equal  to  the  given 
radius.  The  intersection,  O,  is  the  center  of  the  required  arc ;  the  points  of 
tangency  may  be  found  according  to  e.  Note.  There  may  be  four  solutions 
possible. 

(/)  To  bisect  a  given  angle.  Let  ACB  be  the 
given  angle.  Make  CD  and  CE  any  equal  distances. 
Draw  DE.  From  C  draw  CF,  the  bisector,  perpendicular 
to  DE  (B,  Fig.  23). 

(m)  To  draw  an  arc  tangent  to  three  given 
straight  lines.  Let  AB,  BC,  and  CD  be  the  given 
lines.  Bisect  the  angles  ABC  and  BCD  (see  /).  The 
intersection,  O,  of  the  bisectors  is  the  center  of  the 
required  arc. 

(«)  To  draw  an  arc  tangent  to  two  given  straight  lines ;  and  to  a  circle  the 
center  of  which  lies  on  the  bisector  of  their  angle.  Let  AB  and  BC  be  the  given 
lines,  DB  the  bisector  of  the  angle  ABC,  and  F,  lying 
on  DB,  the  center  of  the  given  circle.  At  E,  in  the 
given  circle,  draw  the  tangent  GH  perpendicular  to  DB 
(see  c).  Draw  the  required  arc,  center  O,  tangent  to 
lines  AG,  GH,  and  HC  (see  m). 

(0)  To  draw  an  arc  tangent  to  two  equal  circles,  and  passing  through  a 
point  equally  distant  from  their  centers.  Let  A  and  B  be  the  centers  of  the  given 
circles,  and  P  the  given  point.  Draw,  if  not  already 
given,  line  PC  perpendicular  to  AB  at  its  middle  point. 
Make  PC  equal  to  the  radius  of  either  circle.  Find 
the  center,  O,  of  an  arc  which  would  pass  through  points 
A,  C,  and  B  (see  b).  Point  O  is  the  center  of  the  re- 
quired arc  EPF. 


WORKING  METHODS. 


To  draw  a  scries  of  arcs  of  constant  radius, 
tangent  to  a  series  of  equal  circles.  Find  the  center  O 
according  to  methods  k  or  o.  Since  the  given  circles 
are  equal,  AO  equals  BO.  Using  the  constant  radius 
AO,  find  all  the  centers  O',  O",  etc.;  then,  using  the 
constant  radius  CO,  draw  all  the  required  tangent  arcs. 

(q)  To  draw  a  circular  arc  tangent  to  t^vo  given  straight  lines,  and  passing 
through  a  given  point.  Let  AB  and  BC  be  the  given  lines,  and  P  the  given 
point.  Draw  the  bisector,  BD,  of  the  angle  ABC 
(see  /).  Find  the  required  center,  O,  on  the  line  BD> 
by  trial.  Note.  This  is  typical  of  cases  where  one 
line  through  the  required  center  may  readily  be  drawn, 
but  the  remainder  of  the  geometrical  construction  is  too 
complicated  to  be  easily  remembered. 

(r)  To  draw  a  circular  arc  tangent  to  two  given  circles,  and  passing  through 
a  given  point.  Let  the  circles  be  described  from  the  centers  A  and  B,  as  shown, 
and  let  P  be  the  given  point.  Find  the  center,  O,  of  the 
required  arc  by  trial.  Note.  This  is  typical  of  cases 
where  the  entire  geometrical  construction  is  too  com- 
plicated  to  be  easily  remembered. 

(s)  To  draw  a  regular  hexagon,  given  its  short  diameter.  Let  AB  be  the 
given  diameter.  On  AB  as  a  diameter  draw  a  circle.  Using  the  T-square  and 
3O°-6o°  triangle,  draw  the  sides  of  the  required  hexagon 
tangent  (by  eye)  to  this  circle.  Note.  A  regular  octa- 
gon may  be  similarly  constructed,  using  the  T-square 
and  45°  triangle. 

(f)  In  a  scale  drawing,  to  find  the  radius  of  a  circle,  given  its  diameter.  Lay 
off  the  length  of  the  given  diameter  from  the  scale  which  is  one-half  the  given 
scale ;  this  will  be  the  required  radius.  Note.  This  is  a  convenient  method  for 
dividing  any  scale  measurement  by  2  without  figuring ;  thus,  if  a  dimension  be 
laid  out  from  the  scale  of  3"  =  i  ft.,  then  the  same  dimension  taken  from  the  scale 
of  \\"  =  i  ft.  will  be  one-half  as  long. 


CHAPTER  IV. 


STUDY  PLATES  ON  INSTRUMENTAL  RENDERING  AND  CONSTRUCTION. 

46.  In  order  to  exercise  good  judgment  in  making  a  drawing,  it  is  necessary 
to  grasp  the  leading  points  of  the  required  work  as  a  whole ;  therefore  in  working 
the  following  study  plates  the  student  should  not  proceed  piecemeal — merely 
drawing  as  he  reads — but  he  should  read  all  directions  before  beginning  to  draw. 
Observe  particularly  the  statement  in  the  last  paragraph  of  Art.  35. 

STUDY   PLATE    1. 

For  practice  with  the  pencil,  T-square,  triangles,  scale,  pricker,  and  ruling  pen;  testing, 
tracing;  rendering  of  letters  and  numerals. 

It  is  required  to  make  a  pencil  drawing  from  Plate  6,  and  to  trace  this  drawing. 
The  size  of  the  finished  tracing  is  to  be  14"  x  20". 

I.  THE  PENCIL  DRAWING.  Read  Art.  43.  Use  the  detail  paper  and  the 
4H  pencil  sharpened  as  in  a,  Art.  19.  Make  all  the  lines  fn II,  very  narrow  and 
light,  but  sufficiently  distinct  to  be  readily  seen  through  the  tracing  cloth. 

(a)  Lay  out  the  ruled  border  line.  Draw  the  line  PQ  (KL,  Fig.  76)  and, 
using  the  T-square,  rule  the  lines  in  Fig. 
A.  Using  the  scale  and  the  pricker  (Art. 
36,  e),  lay  off  accurately,  as  many  times 
as  the  length  of  each  line  will  permit,  the 
following  measurements  :  on  line  A,  |" ; 
on  7?  i  "  -  C  7  "  •  D  s"  •  F  3"  •  F  -3-"  • 

uu  u,  y-g      ,   u,  ij2      >  J-^)  f     >  *"t  ^     »       »   16     » 

G,  ^".     On  line  H  lay  off  in  succession 

9_//     15_//    _3_//    _9_//     S'f     2  I//    anf]    _9_//         Tn 
"^f  &     9   ~^  *)     '    1  fi     '    1  fi     'IT     )   "*T  9      I   cm\-i    I  fi      "        -*••!* 

laying  off  the  measurements  on  each  line,  do 
not  move  the  scale.  Test.  Using  T-square 
and  triangle,  drop  a  perpendicular,  as  ac, 
Fig.  76,  from  each  point  of  measurement 
in  line  A.  See  whether  each  perpendicular 
passes  through  the  imaginary  center  of 


e-7" 
*~lg~ 

Hd 

b 

B 

i"r 

e 

C 

4 

i~ 

—  * 

c 
f 

D 

-i"- 

n 

9 

E 

S^ 

0 

h 

F 

\kr$ 

K 

G 

,  9"  ,' 

5I5 

. 
' 

,3' 

9' 

" 

2 

9"—* 

32 

3^ 

I6 

16 

na 

3i 

> 

I6 

Fig.  76. 


each  alternate  point,  as  b,  in  line  B ;  also,  whether  each  perpendicular  from  line  A 
passes  through  each  fourth  point,  as  c,  in  line  C.     Continue  according  to  Fig.  76. 
(/?)     Using  triangle  and  T-square,  rule  the  lines  in  Fig.  B. 

(c]  Fig.  C.     Draw  the  rectangles  to  the  scales  indicated. 

(d)  Figs.  D—J.     Draw  the  horizontal  and  vertical  lines.     Using  triangle  and 

(59) 


60  STUDY  PLATE  i. 

T-square,  draw  the  lines  lettered  AB.  Lay  off  the  \"  spaces  and,  using  the 
proper  triangle  and  T-square,  rule  the  parallel  lines  (see  Fig.  20). 

(e)  Fig.  K.  Draw  the  line  AB,  and  locate  point  C.  Draw  the  equally  spaced 
lines  parallel  to  AB  (see  A,  Fig.  23).  Rule  the  lines  perpendicular  to  AB  (see 
B,  Fig.  23),  and  lay  off  their  length.  Draw  the  lines  from  points  E  and  F  (see 
Fig.  23) ;  terminate  the  lines  by  circular  arcs  as  shown. 

(/)  Using  T-square  and  triangle,  draw  Figs.  L  and  M.  Test.  In  Fig.  L, 
with  the  3O°-6o°  triangle  placed  against  the  T-square,  bisect  the  angles  ;  see  if 
the  bisectors  intersect  in  the  same  point.  In  Fig.  M,  with  the  45°  triangle  placed 
against  the  T-square,  draw  the  diagonals  of  the  square,  upward  from  the  ends  of 
the  base ;  see  if  each  passes  accurately  through  an  upper  corner  of  the  square.* 

(g)  Figs.  N  and  O.  Begin  by  repeating  Figs.  L  and  M.  Find,  by  scale 
measurement,  the  middle  point  of  each  side  of  the  triangle,  Fig.  N,  and  draw  CD, 
BD,  and  AD,  respectively  perpendicular  to  a  side  of  the  triangle.  Lay  off  on 
each  perpendicular  the  measurements  given  on  BD.  Through  these  points,  using 
T-square  and  triangle,  draw  the  sides  of  the  interior  triangles.  Test.  Produce  CD, 
BD,  and  AD,  and  see  if  the  alignments  of  the  corners  of  the  triangles  are  accurate. 
Fig.  O.  Find  by  scale  measurement  the  centers  C  and  B  of  two  sides  of  the 
square.  Draw  the  diameters,  CD  and  AB,  of  the  square.  On  each  semi-diameter 
lay  off  the  measurements  given  at  C.  Through  these  points  draw  the  sides  of  the 
interior  squares.  Test.  Draw  the  diagonals  of  the  outer  square  and  see  if  they 
pass  through  the  center  of  the  square,  as  located  by  the  diameters,  and  also  if  they 
pass  through  the  corners  of  the  inner  squares. 

(k)  Fig.  P.  Construct  the  hexagon ;  draw  the  sides  in  succession,  and  lay 
off  the  length  of  each  with  the  scale.  Test.  Connect  the  opposite  angles  ;  see  if 
the  diagonals  thus  obtained  intersect  in  the  same  point. 

(i)  Fig.  Q.  Draw  AB.  Using  T-square  and  triangle,  complete  the  hexagon 
without  further  scale  measurement.  Test.  Measure  with  the  scale  each  side  of 
the  hexagon,  and  see  if  all  have  the  same  length. 

(/)  "Plate  i,"  the  student's  name,  the  date,  and  all  lettering  and  dimensions 
on  Plate  6  are  to  be  given  on  the  tracing,  and  rendered  directly  in  ink.  In  an- 
ticipation of  this  work,  the  position,  judged  by  eye,  of  the  lettering  and  dimensions 
should  be  indicated  on  the  preliminary  drawing.  Also  suggest  lightly  and  rapidly 
the  size,  form,  and  spacing  of  the  letters  and  numerals.  For  " Plate"  students 
name,  date,  and  Fig.  A,  Fig.  B,  etc.,  draw  two  guide  lines  ;  for  all  other  lettering  and 
the  dimensions  use  but  one  guide  line.  Suggest  according  to  the  general  idea  shown 
in  A  and  B,  Fig.  58.  Follow  the  forms  of  the  letters  and  numerals  in  Figs.  A 
and  F,  Plate  5  ;  but,  when  one  guide  line  is  used,  determine  sizes  wholly  by  eye. 

*  If  the  results  are  not  accurate,  it  should  be  found  whether  the  fault  lies  in  the  triangle  (see  Art. 
6,  a,  b,  and  c). 


(0   0 


~_nn:jm^nr- :  co  / 

A  .      / 


STUDY  PLATE  i.  63 

II.  THE  TRACING.  Use  tracing  cloth;  and  work  on  the  dull  surface. 
Smooth  out  the  cloth  so  it  will  be  as  flat  as  possible,  and  fasten  with  four  additional 
thumb  tacks  placed  midway  between  the  corners.  See  that  the  ink  is  black. 
If  the  cloth  does  not  take  the  ink  well,  use  chalk  (Art.  17).  The  lines  of  the 
tracing  should  cover  the  pencil  lines  accurately.  Ink  the  lines  drawn  frCm  E  and 
F,  Fig.  K,  as  shown  (see  Art.  44,  /). 

(k]  Indicate  the  scale  measurements  laid  off  in  the  pencil  drawing  on  lines 
A — H,  Fig.  A,  by  ruling  through  the  center  of  each  point  of  division  a  very  narrow 
line  perpendicular  to  and  extending  about  -jL"  above  and  below  the  given  line. 
Make  the  lines  A — /,  Fig.  A,  full,  and  of  the  width  given  in  A,  Fig.  55.  Make  the 
lines  K — O,  Fig.  A,  correspond  to  the  lines  B — F,  Fig.  55.  Make  the  lines  R —  W, 
Fig.  B,  like  the  lines  D—J,  Fig.  55.  Make  incidental  lines — as  AB,  Fig.  D,  and 
the  arcs  in  Fig.  K — like  A  or  B,  Fig.  55.  Ink  all  remaining  lines  according  to 
D,  Fig.  55.  The  line  width  of  the  ruled  border  should  be  slightly  greater  than 
that  of  the  line  D,  Fig.  55.  Test.  Measure  with  the  scale  the  divisions  of  lines 
A — Ht  Fig.  A  ;  see  if  they  correspond  to  the  dimensions,  Fig.  76. 

(/)  Read  Art.  40,  a;  then  stroke  render,  with  the  ball-point  pen,  the  dimen- 
sions and  all  letters  including  "Plate  /,"  name  of  student,  date,  "Fig.  A"  "Fig. 
B,"  etc.  Rule  the  extension  lines,  then  rule  the  dimension  lines.  Put  in  the  arrow 
heads,  with  the  ball-point  pen.  Letter  rapidly,  but  careftdly. 

(m)  Read  Art.  33,  b,  c,  and  d.  Erase  the  lines  drawn  from  points  E  and  F, 
Fig.  K ;  the  dimensions  locating  these  points  ;  and  the  letters  " E"  and  "F."  Use 
an  erasing  shield.  Relocate  the  points  E  and  .Fon  the  tracing  at  i-j5g"  from  AB. 
Place  the  new  points  over  the  original  ones  on  the  pencil  drawing,  and  retrace  the 
radiating  lines.  Change  the  dimensions  to  correspond  to  the  new  location  of  E  and 
F,  and  replace  the  letters.  Restore  any  lines  injured  in  making  these  alterations. 

(;/)  Hand  in  the  pencil  drawing  and  the  tracing,  each  trimmed  to  size.  Do 
not  roll  or  fold  them,. 

STUDY   PLATE   2. 

For  accuracy  and  speed  in  the  use  of  the  compass,  dividers,  and  French  curve;  testing; 
tracing;  the  rendering  of  letters  and  numerals. 

Read  all  of  the  following  directions  before  beginning  to  draw. 

It  is  required  to  make  a  drawing,  from  Plate  7,  to  be  traced.  The  size  of  the 
finished  tracing  is  to  be  14"  x  20",  the  ruled  border  line  12"  x  18". 

I.  THE  PENCIL  DRAWING.  Use  the  detail  paper  and  the  4H  pencil.  Make 
lines  full,  narrow,  and  light,  but  so  they  can  be  readily  seen  when  tracing. 

(a)     Fig.  A.     Describe  circle  A.     Rule  a  line  from  the  center  to  the  circum- 


64  STUDY  PLATE  2. 

ference,  and  on  this  line  lay  off  the  spacing  of  the  interior  circles.  Beginning 
with  the  smallest,  I"  in  diameter,  describe  the  circles  according  to  a,  Art.  27. 
From  the  same  center,  using  the  lengthening  bar,  draw  the  arcs,  Fig.  C  (Art.  27,  b\ 
(b]  Fig.  B.  Work  the  following  steps  very  accurately.  Draw  AB,  and  locate 
the  center,  C,  by  scale  measurement.  Using  only  the  T-square  and  the  3O°-6o° 
triangle  placed  against  the  T-square,  draw  the  hexagon,  its  diameters,  and  its  diag- 
onals. Distant  f"  from  A,  locate  point  H,  and,  with  C  as  center,  describe  the 
circle  OHK.  With  £ "  radius,  centers  on  circle  OHK,  describe  the  circles  tangent 
to  the  sides  of  the  hexagon.  Establish  the  points  of  tangency,  as  P,  Q,  and  R,  by 
drawing,  with  C  as  center,  the  circle  through  point  P,  which  is  the  intersection  of 
HK  and  CT.  Tests.  With  C  as  center,  radius  CA,  describe  a  circle;  see  if  the  im- 
aginary center  lines  of  the  three  tangent  lines  at  A,  G,  E,  B,  F,  and  D,  intersect  in 
a  point  (Fig.  52).  With  f"  radius,  Cas  center,  draw  a  circle;  see  if,  in  its  intersec- 
tion with  each  diameter  of  the  hexagon,  it  is  tangent  to  each  of  the  six  equal  circles. 
If  the  results  in  the  foregoing  constructions  are  found  to  be  inaccurate,  all  lines 
should  be  erased,  the  line  AB  moved  I"  to  the  left,  and  the  construction  repeated. 

(c)  Fig.  D.     Draw  of  indefinite  length  the  line  LH,  and  locate  lines  A — F. 
With  the  hair-spring  dividers,  and  according  to  a,  Art.  29,  and  f,  Art.  36,  space 
the  line  D  into  13  equal  parts  ;  B  into  9  ;  and  C,  7.     With  the  bow  spacers  divide 
equally  as  follows  :  A  into  13  parts ;  £,  9 ;  F,  7.     Test.     Produce  JK  to  cut  LH 
in  L.     Pass  an  edge  of  a  triangle  successively  through  L  and  each  point  in  the 
line  D.     Draw  short  lines  where  the  edge  crosses  line  A,  and  note  whether  these 
lines  pass  exactly  through  the  points  in  A  as  obtained  with  the  spacers.     Test  in 
like  manner  the  points  in  lines  B  and  E,  and  in  lines  C  and  F. 

(d)  Fig.  E.     Draw  the  circles,  circular  arcs,  and  line  EM.     With  the  hair- 
spring dividers,  and  starting  at  line  EM,  space  the  circles  A  and  B  each  into  19 
equal  parts.     With  the  bow  spacers,  starting  at  line  EM,  divide  circles  C  and  D  each 
into  19  equal  parts.     Test.     Draw  very  accurately  from  center  E  to  each  point  of 
division  in  circle  A  ;  see  if  each  line  passes  through  the  centers  of  the  correspond- 
ing divisions  in  circles  B,  C,  and  D. 

Draw  EG  through  point  14.,  Fig.  E.  With  the  hair-spring  dividers,  divide 
arc  HN  into  5  equal  parts;  JO  and  LQ  each  into  9;  KP  and  MG  each  into  7 
parts.  Tests.  Draw  from  center  E,  through  points  75,  16,  77,  and  18,  circle  A,\ 
see  if  these  lines  produced  pass  through  the  centers  of  the  points  of  division  in  arc 
HN.  From  center  E  draw  through  the  points  of  division  in  JO,  and  produce  the 
lines  to  intersect  LQ;  see  if  the  lines  pass  through  the  centers  of  the  points  of 
division  in  LQ.  From  center  E  draw  through  the  points  of  division  in  MG;  see 
if  the  lines  pass  through  the  centers  of  the  points  of  division  in  KP. 

(e)  Locate  a  point  on  the  lower  horizontal  portion  of  the  ruled  border  line, 


(65) 


64  STUDY  PLATE  2. 

ference,  and  on  this  line  lay  off  the  spacing  of  the  interior  circles.  Beginning 
with  the  smallest,  |"  in  diameter,  describe  the  circles  according  to  a,  Art.  27. 
From  the  same  center,  using  the  lengthening  bar,  draw  the  arcs,  Fig.  C  (Art.  27,  £). 

(b]  Fig.  B.  Work  the  following  steps  very  accurately.  Draw  AB,  and  locate 
the  center,  C,  by  scale  measurement.  Using  only  the  T-square  and  the  3O°-6o° 
triangle  placed  against  the  T-square,  draw  the  hexagon,  its  diameters,  and  its  diag- 
onals. Distant  f"  from  A,  locate  point  H,  and,  with  C  as  center,  describe  the 
circle  OHK.  With  f "  radius,  centers  on  circle  OHK,  describe  the  circles  tangent 
to  the  sides  of  the  hexagon.  Establish  the  points  of  tangency,  as  P,  Q,  and  R,  by 
drawing,  with  C  as  center,  the  circle  through  point  P,  which  is  the  intersection  of 
HK  and  CT,  Tests.  With  Cas  center,  radius  CA,  describe  a  circle;  see  if  the  im- 
aginary center  lines  of  the  three  tangent  lines  at  A,  G,  E,  B,  F,  and  D,  intersect  in 
a  point  (Fig.  52).  With  f"  radius,  C  as  center,  draw  a  circle;  see  if,  in  its  intersec- 
tion with  each  diameter  of  the  hexagon, it  is  tangent  to  each  of  the  six  equal  circles. 
If  the  results  in  the  foregoing  constructions  are  found  to  be  inaccurate,  all  lines 
should  be  erased,  the  line  AB  moved  \"  to  the  left,  and  the  construction  repeated. 

(c)  Fig.  D.  Draw  of  indefinite  length  the  line  LH,  and  locate  lines  A — F. 
With  the  hair-spring  dividers,  and  according  to  a,  Art.  29,  and/,  Art.  36,  space 
the  line  D  into  1 3  equal  parts  ;  B  into  9  ;  and  C,  7.  With  the  bow  spacers  divide 
equally  as  follows  :  A  into  13  parts;  £,9;  F,  7.  Test.  Produce  JK  to  cut  LH 
in  L.  Pass  an  edge  of  a  triangle  successively  through  L  and  each  point  in  the 
line  D.  Draw  short  lines  where  the  edge  crosses  line  A,  and  note  whether  these 
lines  pass  exactly  through  the  points  in  A  as  obtained  with  the  spacers.  Test  in 
like  manner  the  points  in  lines  B  and  E,  and  in  lines  C  and  F. 

(d}  Fig.  E.  Draw  the  circles,  circular  arcs,  and  line  EM.  With  the  hair- 
spring dividers,  and  starting  at  line  EM,  space  the  circles  A  and  B  each  into  19 
equal  parts.  With  the  bow  spacers,  starting  at  line  EM,  divide  circles  Cand  D  each 
into  19  equal  parts.  Test.  Draw  very  accurately  from  center  E  to  each  point  of 
division  in  circle  A  ;  see  if  each  line  passes  through  the  centers  of  the  correspond- 
ing divisions  in  circles  B,  C,  and  D. 

Draw  EG  through  point  14,  Fig.  E.  With  the  hair-spring  dividers,  divide 
arc  HN  into  5  equal  parts;  JO  and  LQ  each  into  9;  KP  and  MG  each  into  7 
parts.  Tests.  Draw  from  center  E,  through  points  75,  16,  17,  and  18,  circle  A,\ 
see  if  these  lines  produced  pass  through  the  centers  of  the  points  of  division  in  arc 
HN.  From  center  E  draw  through  the  points  of  division  in  JO,  and  produce  the 
lines  to  intersect  LQ;  see  if  the  lines  pass  through  the  centers  of  the  points  of 
division  in  LQ.  From  center  E  draw  through  the  points  of  division  in  MG;  see 
if  the  lines  pass  through  the  centers  of  the  points  of  division  in  KP. 

(e)     Locate  a  point  on  the  lower  horizontal  portion  of  the  ruled  border  line, 


(0 


CO 


o 


o 


STUDY  PLATE  2.  69 

6"  from  the  right-hand  end.  Cut  small  triangular  holes  in  Plate  8,  so  that  the 
line  AB  can  be  placed  accurately  over  the  border  line  of  the  drawing,  with  the 
point  c  at  the  located  point.  Read  Art.  20,  b.  Lay  the  book  on  the  drawing, 
and  place  AB  and  c,  as  just  described.  Pricking  through  the  plate,  locate  the  axes 
of  the  ellipses,  and  points  in  the  curves,  Fig.  F.  Locate  as  many  of  the  latter  as 
are  necessary  to  obtain  smooth  curves,  but  do  not  exaggerate  the  number.  It  is 
evident  that  the  points  should  be  taken  closer  together  for  the  more  sharply  curv- 
ing portions  of  a  line  than  for  the  flatter  portions.  It  is  suggested  that  the  dis- 
tances range  from  Jg"  to  \"  according  to  the  amount  of  curvature.  Rule  the 
axes  of  the  ellipses.  Read  Art.  25,  a.  In  the  ellipses,  suggest  the  portions  of 
each  at  the  extremities  of  the  axes  and  then  fill  in  the  remaining  portions. 

(/)     Suggest  all  lettering  and  dimensions  according  to  Study  Plate  i,j. 

II.  THE  TRACING.  Use  tracing  cloth,  and  work  on  the  dull  surface.  See 
that  the  ink  is  black.  Trace  the  drawing  accurately.  Proceed  as  follows  : 

(g)  Fig.  A .  Ink,  before  the  center  is  enlarged,  circles  N  and  O  in  line 
similar  to  A,  Fig.  55.  Make  the  circles  G — M  according  to  A — F,  Fig.  55;  re- 
peat for  the  circles  A — F.  Fig.  C.  Ink  A — F  according  to  D — -J,  Fig.  55. 
Fig.  B.  The  line  of  the  hexagon  and  of  the  resultant  circles  should  be  the  same 
as  D,  Fig.  55.  The  other  lines  of  this  figure  should  correspond  to  line  A,  Fig,.  55, 
and  may  be  drawn  with  red  or  black  ink.  Figs.  D  and  E.  Rule  (in  red  or  black) 
the  division  lines  drawn  in  the  tests,  before  inking  the  given  lines.  The  division 
lines  should  be  very  narrow,  and  extend  ^",  judged  by  eye,  from  each  side  of  the 
given  line.  Ink  the  remaining  lines  of  the  several  figures  according  to  D,  Fig.  55. 
Make  the  border  line  slightly  heavier  than  line  Z>,  Fig.  55. 

(//)  Render  the  lettering,  dimensions,  dimension  and  extension  lines,  and 
arrow  heads  according  to  /,  Study  Plate  i . 

(z)     Erase  and  redraw  the  ellipse  D,  but  place  it  I"  to  the  left  (Art.  33,  d}. 

(J]  Hand  in  the  pencil  drawing  and  the  tracing,  each  trimmed  to  size.  Do 
not  roll  or  fold  them. 

STUDY  PLATE   3. 

For  practice  in  rendering  freehand  lines,  cross  hatching,  and  line  shading. 

Read  all  of  the  follo^cving  directions  before  beginning  to  dra^v. 

It  is  required  to  make  a  preliminary  drawing  in  pencil,  and  to  render  the  con- 
ventions, Plate  4,  p.  41,  directly  in  ink  on  tracing  cloth.  The  tracing  is  to  be 
14"  x  20"  and  the  ruled  border  13"  x  19". 

I.  THE  PENCIL  DRAWING.  Use  the  duplex  detail  paper  and  the  4H  pencil. 
Draw  the  outlines  of  Figs.  A — D.  Read  Art.  38,  and  then  suggest  the  breaks  and 
graining,  Fig.  A.  In  the  upper  left-hand  corner  of  each  rectangle,  Fig.  C,  rule  four 
or  five  lines  representative  of  the  cross  hatching  in  the  corresponding  rectangle, 


yo  STUDY  PLATE  3. 

to  be  used  as  a  gage  when  cross  hatching  on  the  tracing.  Make  the  line  width 
and  spacing  twice  as  great  as  in  Fig.  C.  Obtain  the  widths  thus  :  On  a  strip  of 
thin  paper,  with  a  very  sharp  pencil,  and  working  under  the  reading  glass,  start  a 
line  width  with  a  short  narrow  line  made  freehand ;  then  gradually  increase  this 
line  until  it  is  of  the  required  width  judged  by  eye.  Lay  off  twice  the  space  be- 
tween the  lines  in  Fig.  C,  and  then  indicate  the  required  width  for  a  second  line 
of  the  cross  hatching.  Transfer  the  widths  from  the  strip  to  the  drawing,  making 
the  width  of  the  lines  of  the  gage  exactly  equal  to  them. 

II.  THE  TRACING,  (a)  Use  tracing  cloth  ;  work  on  the  dull  surface.  See 
that  the  ink  is  black.  Trace  the  ruled  outlines  of  all  of  the  figures  except  V- —  V" 
and  W- — W" >  Fig.  D.  Make  the  width  of  these  lines  the  same  as  D,  Fig.  55, 
leaving  the  shade  lines  (Art.  58)  to  be  added  later  on.  Ink  the  breaks  and  the 
cross  hatching  on  the  breaks  of  the  cylinders  freehand  ;  use  a  ball-point  pen.  Do 
the  graining ;  use  the  Gillott's  No.  303  pen.  Proceeding  strictly  as  directed  in 
Art.  38,  b,  cross  hatch  the  rectangles.  Trace  the  lines  of  the  gage,  and  then  keep 
the  line  widths  and  spacing  of  the  gage  throughout,  wholly  by  eye.  As  the 
cross  hatching  proceeds,  it  should  be  frequently  compared  with  the  portion  cover- 
ing the  gage.  Read  Art.  38,  c.  Pencil,  on  the  tracing,  the  gages  for  the  line 
shading,  Fig.  D.  It  is  best  not  to  ink  the  contour  elements  before  shading,  as 
the  widths  of  these  lines  may  need  to  be  modified  so  as  to  preserve  the  gradation 
of  the  shading.  The  rendering  of  each  convention  should  be  practiced  on  spare 
tracing  cloth  before  attempting  it  on  the  required  drawing.  Add  the  shade  lines ; 
make  their  width  the  same  as  line  E,  Fig.  5  5 . 

(b)  Lettering.     Letter  "  Plate  3  "  (drawn  letters),  your  name,  and  the  date 
(stroke  rendered). 

(c)  Hand  in  the  pencil  drawing  and  the  tracing,  each  trimmed  to  size.     Do 
not  roll  or  fold  them. 

STUDY  PLATE   4. 
For  practice  in  strictly  accurate  pencil  construction  and  finished  rendering  in  ink. 

Read  all  of  the  following  directions  before  beginning  to  draw. 

It  is  required  to  make  a  very  accurate  and  finished  drawing  in  ink,  from 
Plate  9.  The  size  is  to  be  14"  x  20",  the  ruled  border  12"  x  18". 

I.  THE  PENCILING,  (a)  Use  Whatman's  hot-pressed  paper,  a  6H  pencil, 
and  6H  leads  in  the  compass  and  bow  compass.  Lay  out  the  ruled  border  line. 
Draw  the  center  lines  VWand  XY,  placing  the  sprockets  ioi"  apart  instead  of  the 
true  distance,  18".  Draw  the  center  line  of  the  chain,  which  should  be  broken  as 
shown.  With  radius  3^"*  and  P  as  a  center,  draw  the  pitch  circle,  J,  of  the  front 

*The  diameters  6}^",  Fig.  A,  and  2$J",  Fig.  B,  are  the  nearest  fractional  equivalents  of  the  true 
(decimal)  pitch  diameters  given  on  the  plate  (see  table  at  the  end  of  the  book). 


STUDY  PLATE  4.  73 

sprocket,  Fig.  A.  Draw  line  GH tangent  to  circle  /.  Tangent  to  GH,  draw  the 
pitch  circle,  N,  of  the  rear  sprocket,  Fig.  B.  (Lay  off  the  diameter,  2f£",  on  the 
centre  line  XY,  and  find  the  centre  by  bisecting). 

(b)  To  find  the  direction  of  the  lower  portions,  TU  arid  RS,  of  the  cJtain. 
Tack  a  piece  of  paper  over  the  drawing  so  as  not  to  cover  the  lower  half  of  the  cir- 
cles J  and  N.     (Do  not  place  the  tacks  inside  the  boundary  of  the  finished  plate.) 
On  this  extra  sheet  make  a  half-size  diagram  of  the  center  lines,  similar  to  Fig.  E, 
placing  line  G'H'  parallel  to  GH.     Draw  the  common  tangent,  T'S' ;  then,  parallel 
to  T'S',  draw  the  required  tangents,  TU  and/? 5.     (Do  not  draw  this  diagram  di- 
rectly on  the  finished  drawing,  as  the  necessary  erasure  will  mar  the  paper.) 

(c)  The  teeth  of  the  sprockets  and  the  links  of  the  chain.     It  will  be  seen 
(Figs.  C  and  F)  that  the  chain  is  composed  of  alternate  closed  and  open  links,  and 
that  the  teeth  mesh  into  the  latter.     The  inside  length  of  an  open  link  determines 
the  width,  Y'Z,  Fig.  Ft  of  the  teeth,  while  the  shape  of  the  interior  determines  the 
curves  X',  X',  of  the  teeth.     The  spaces,  ZY',  between  the  teeth,  must  equal  the 
total  length  of  a  closed  link. 

Construction:  the  teeth  of  the  front  sprocket.  Starting  at  point  G,  Fig.  A, 
with  the  hair-spring  dividers  space  the  pitch  circle  accurately  into  21  equal  parts 
(a,  Art.  29),  and,  to  identify  the  points,  enclose  each  point  in  a  small  freehand 
circle.  Let  the  first  two  spaces,  G"  V  and  V  V",  Fig.  F,  be  typical  of  all  of  the 
21  spaces.  Take  in  the  bow  spacers  the  given  distance  between  the  centers  of 
an  open  link  (that  is,  T9g"),  and  lay  it  off  from  points  G"  and  V  ;  this  establishes 
the  centers  of  the  pins  of  all  the  links.  With  •£%"  radius,  centers  G",  W ,  V ', 
W",  and  V",  draw  (all  the  way  around  the  pitch  circle)  complete  circles  represent- 
ing the  ends  of  the  links ;  these  circles  determine  the  curves  X',  X't  of  the  teeth. 
With  radius  if"  (Ty  minus  one-half  of  ^g")  describe,  from  the  centers  of  the 
pins,  the  curves  Y'  and  Z  of  the  teeth.  The  extremities  of  the  teeth  and  the 
bottoms  of  the  spaces  are  portions  of  the  circles  abc  and  def,  Fig.  F,  which  are 
drawn  according  to  the  measurements  given  in  Fig.  A. 

The  teeth  of  the  rear  sprocket.  Starting  at  point  H,  Fig.  B,  divide  the  pitch 
circle  accurately  into  8  equal  parts.  Draw  the  teeth  according  to  the  directions 
given  for  the  teeth  of  the  front  sprocket. 

The  chain.  The  pins  and  ends  of  the  links  for  the  portions  of  the  chain  in 
contact  with  the  sprockets  are  already  drawn.  Locate  the  centers  of  the  pins  for 
the  straight  portions  of  the  chain,  and  draw  complete  circl'es  determining  the  ends 
of  the  links.  Find  the  radii  for  the  sides  of  the  links  (o,  Art.  45) ;  find  all  the 
centers  for  arcs  that  have  the  same  radius,  and  draw  all  such  arcs  as  one  operation 
(/,  Art.  45). 

(d)  Draw  the  circles  containing  the  centers  of  the  holes  in  the  webs  of  the 
sprockets,  and  space  each  circle  for  the  number  of  holes  shown. 


74  STUDY  PLATE  4. 

(e)  Locate  Figs.  C  and  D.  The  section,  Fig.  D,  of  the  rear  sprocket  is  a  true 
section  taken  on  a  line  drawn  through  the  center  of  Fig.  B,  downward  to  the  right, 
and  just  clearing  the  hole,  in  the  web,  which  cuts  KM.  Otherwise,  all  lines  in 
Figs.  C  and  D,  not  located  by  the  given  measurements,  are  to  be  projected  from  Figs. 
A  and  B.  The  chain  is  projected  from  the  horizontal  portion. 

(/)  Complete  the  penciling.  Look  over  the  drawing,  and  see  that  no  details 
have  been  omitted.  Do  not  indicate  the  dimensions  and  lettering  before  inking. 

II.  THE  INKING,  (g)  Ink  with  special  care.  First  make  the  width  of  all 
lines  equal  to  that  of  A,  Fig.  55.  Omit  the  cross-hatching  for  the  present. 

(/i)  Shade  lines.  Read  Arts.  44,  g,  and  58.  Make  the  line  width  the  same 
as  in  D,  Fig.  55.  This  width  should  be  increased  wherever  a  line  may  look  weak, 
and  should  be  decreased  if  necessary  to  prevent  lines  from  running  together. 

(2)  Lettering  and  dimensions.  All  lettering  and  all  dimensions  given  on  Plate 
9,  except  those  marked  *,  should  appear  on  the  student's  drawing.  The  letters  and 
numerals  should  be  drawn  (Art.  41),  not  stroke  rendered.  Rule  guide  lines  ac- 
cording to  Figs.  58  and  62  ;  make  the  size  of  the  letters  and  numerals  the  same  as 
in  Fig.  E,  Plate  5.  Rule  guide  lines  for  the  title,  according  to  the  measurements 
given  on  the  plate,  and  balance  the  title  on  the  vertical  center  line  of  the  plate 
(b,  Art.  41).  Letter  "Plate  4,"  your  name,  and  the  date.  (See  Art.  39.) 

(/)     Cross-hatch  the  sections,  and  erase  pencil  lines  throughout  the  drawing. 

Do  not  roll  or  fold  the  drawing. 

STUDY  PLATE  5. 

For  precise  spacing  with  the  dividers  and  bow  spacers ;  strictly  accurate  scale  measurement 
and  penciling ;  finished  rendering  in  ink;  lettering  and  dimensioning. 

Read  all  the  following  directions  before  beginning  to  draw. 

It  is  required  to  make  a  strictly  accurate  drawing  of  the  spur  gear,  Plate  16. 
The  size  of  the  drawing  is  to  be  10"  x  14",  the  ruled  border  line  8"  x  12".  The 
"  Scale  Half  Size"  on  the  plate  indicates  the  scale  of  the  required  drawing.  As 
dimensions  on  a  drawing  always  indicate  true  measurement,  it  is  evident  that  the 
dimensions  on  the  plate,  except  these  marked*,  must  be  divided  by  2.  The  dia- 
gram, Fig.  C,  is  given  to  supplement  the  directions  which  follow,  and  should  not 
appear  in  the  student's  drawing ;  note  that  corresponding  lines  in  Figs.  A  and  C  are 
similarly  lettered. 

I.  THE  PENCILING,  (a)  Use  Whatman's  hot-pressed  paper,  and  the  6H 
pencil.  Make  all  lines  full  and  very  narrow.  Lay  out  the  border  line,  and  draw 
the  center  lines  MO  and  DP,  located  as  shown  on  the  plate.  With  point  N  as 
center,  radius  3f"  (equals  13!"  divided  by  4),  draw  the  pitch  circle  G  (Gf , 
Fig.  C). 

(b}     Dividing  the  pitch  circle.      Starting   at  point  a,    Fig.   C,  lying  in   the 


STUDY  PLATE  5.  77 

center  line  D'P',  divide  with  great  precision  (/,  Art.  36)  the  pitch  circle  into  108 
equal  parts,  each  to  contain  one  tooth  and  one  space  (between  adjacent  teeth).  As 
it  is  next  to  impossible  to  divide  a  circle  directly  into  so  great  a  number  of  equal 
parts,  first  divide  the  circle  very  accurately  into  6  equal  parts  (see  points  a, 
R,  S,  P' ,  T,  and  U,  Fig.  C) ;  for  this,  do  not  use  the  3O°-6o°  triangle,  but  lay  off 
the  distances  with  the  hair-spring  dividers  set  to  the  radius  of  the  pitch  circle.  To 
see  that  the  measurement  is  exact,  test  the  division  by  stepping  the  dividers  in  an 
opposite  direction  before  indenting  the  points ;  to  identify  the  points,  draw  very 
lightly  a  small  freehand  circle  about  each.  Using  the  bow  spacers,  divide  each  of 
the  six  divisions  into  1 8  equal  parts  ;  test  the  divisions  by  restepping  in  an  opposite 
direction ;  draw  a  freehand  circle  about  each  point  of  division. 

(c)  The  width  of  the  teeth.     Let  ac  and  ce,  Fig.  C,  represent  the  first  two  of 
the  1 08  spaces.     In  the  present  drawing  the  widths  of  the  teeth  are  made  equal  to 
the  spaces  between  them.     Take  one-half  of  ac  in  the  bow  spacers,  and,  starting  at 
point  a,  lay  off  this  distance  from  each  of  the  points  marking  the   108  spaces, — as 
shown  for  the  teeth  at  ab,  cd,  and  ef.     In  order  that  the  space  divisions  may  not 
be  mistaken  for  teeth  divisions  —  not  an  uncommon  mistake  —  each  tooth  division 
should  be  identified  by  a  very  light  freehand  line,  as  shown  between  c  and  d,  Fig.  C. 

(d)  The  outline  of  the  teeth.     The  extremities  of  the  teeth  and  the  bottom 
of  the  spaces  are  circular  arcs ;  in  the  present  case  the  sides  of  the  teeth  are  also 
circular  arcs.     The  centers  of  the  sides  of  the  teeth  lie  in  the  circle  J.     Draw 
circles  F,  H,  and  J,  according  to  the  measurements  in  Fig.  A.     To  complete  the 
teeth  in  pencil :  With  the  same  radius  throughout  (namely,  one-half  of  1 |-"),  center 
at  the  point  marking  a  side  of  a  tooth,  as  a,  Fig.  C,  cut  the  circle  .of  centers,  /',  at 
point  //.     With  center  h,  draw  the  side  of  the  tooth  through  point  a.     With  center 
at  the  point  b,  marking  the  opposite  side  of  the  tooth,  cut  the  circle  of  centers  at 
point  j.     With  center/,  draw  the  side  of  the  tooth.     Draw  each  tooth  in  a  similar 
manner. 

(<?)  The  arms  of  the  gear.  Draw  circle  K',  and  the  center  lines  RT  and  SU 
of  the  arms.  The  widths  of  each  arm  are  measured  in  lines,  perpendicular  to  the 
center  line  of  the  arm,  located  from  the  center  of  the  gear.  With  radii  equal  to  one- 
half  of  5f",  and  one-half  of  i|",  respectively,  draw  the  circles  Fand  W.  Tangent 
to  these  circles,  draw  the  lines  upon  which  to  lay  off  the  widths  of  the  arms.  (Use 
the  3O°-6o°  triangle  to  draw  the  perpendiculars  to  the  center  lines  RT  and  St7.) 
Lay  off  the  arm  widths,  and  draw  the  sides  of  the  arm  produced,  as  kn  and  mo. 

Make  the  circular  arcs  (fillets)  connecting  adjacent  sides  of  the  inner  ends  of 
the  arms,  of  T3g"  radius  (not  given  on  the  plate) ;  draw  them  according  to  «,  Art.  45. 
Make  the  fillets,  at  the  outer  ends  of  the  arms,  of  \"  radius  (not  given  on  the  plate)  ; 
draw  them  according  to/,  Art.  45. 


78  STUDY  PLATE  5. 

(/)  The  section  of  the  gear,  Fig.  B,  is  taken  on  line  DP  (Fig.  A) .  Locate 
line  EQ  as  shown  on  the  plate.  All  parts  not  determined  by  the  given  dimensions 
must  be  projected  from  Fig.  A.  Make  the  radius  of  the  fillets  Ty  (not  given  on 
the  plate) ;  draw  them  according  to/,  Art.  45. 

(g)  Complete  Fig.  A  ;  the  diameter  of  the  hub  must  be  taken  from  Fig.  B. 
Draw  the  cross  section  of  the  arm  as  shown,  Fig.  A,  taking  its  width  from  the  sec- 
tion, Fig.  B. 

(li)  Do  not  cross  hatch  the  section,  or  indicate  the  measurements  and  letter- 
ing before  inking  the  drawing. 

II.  THE  INKING.  (?)  Ink  the  drawing  with  special  care  ;  make  all  lines  at 
first  of  the  same  width,  and  equal  to  that  of  the  line  A,  Fig.  55. 

(/)  Shade  lines.  Add  the  shade  lines;  make  their  width  equal  to  that  of  the 
line  D,  Fig.  55  ;  render  them  according  to  Art.  44,^.  (Also  see  Art.  58.) 

(k)  Lettering  and  dimensions.  All  dimensions  given  on  Plate  10,  except 
those  marked  *,  should  appear  on  the  student's  drawing.  The  letters  and  nu- 
merals should  be  drawn  (Art.  41),  not  stroke  rendered.  Rule  guide  lines 
according  to  Figs.  58  and  62  ;  make  the  size  of  the  numerals  the  same  as  in  Fig. 
Et  Plate  5.  Rule  guide  lines  for  the  title,  according  to  the  measurements  given  on 
the  plate,  and  balance  the  title  on  the  vertical  center  line  of  the  plate  (b,  Art.  41) 
Letter  "  Plate  5,"  your  name,  and  the  date. 

(/)     Erase  pencil  lines  throughout  the  drawing. 

Do  not  roll  or  fold  the  drawing. 


CHAPTER   V. 

GEOMETRICAL  CONSTRUCTION. 

47-  The  following  problems  are  given  for  further  practice  in  precise  rendering 
and  for  their  practical  application.  It  should  be  understood  that  the  use  of  such 
problems  is  not  necessarily  confined  to  the  drawing  room  or  to  drawings  of  the  usual 
sizes.  A  good  example  of  this  may  be  found  in  surveying,  where  problems  are  often 
worked  out  on  a  large  scale,  the  straight  lines  being  run  out  with  the  transit,  which 
corresponds  to  the  straight-edge  in  drawing,  and  the  circular  arcs  swung  with  the 
chain,  or  tape  as  a  substitute  for  the  drawing  compass.  Likewise,  the  landscape 
gardener  lays  out  geometrical  figures  directly  on  the  ground,  stretching  the  tape  for 
a  straight-edge,  and  describing  arcs  with  the  aid  of  tape  and  measuring  pins.  In  the 
mechanic  arts,  the  workman  may  need  to  lay  out  a  construction  to  the  actual  size  of 
his  work,  on  wood,  metal,  or  the  floor  of  the  shop ;  in  large  work  substituting  chalk 
line  for  straight-edge,  and  striking  the  arcs  with  a  piece  of  chalk  held  at  the  end  of 
a  string  or  a  strip  of  wood  swung  from  a  nail  as  center. 

PENCILING.  Use  a  6H  pencil,  make  all  lines  full,  and  draw  with  the  greatest 
accuracy  possible.  For  appearance,  intersecting  arcs  should  be  made  of  equal 
length,  and  should  be  at  right  angles. 

Instead  of  always  following  a  geometrical  method  to  its  limit,  it  is  better  in 
some  cases  to  rely  upon  instrumental  methods.  For  example,  parallels  (as  in 
Prob.  1 3)  may  be  drawn  by  sliding  the  triangles  (Art.  23) ;  circular  arcs  may  be 
divided  (as  in  the  case  of  D5B,  Prob.  27)  with  the  bow  spacers;  and  horizontals 
and  perpendiculars  (as  in  Prob.  44)  may  be  drawn  with  the  T-square  and  triangle. 

When  practicable,  final  results  should  always  be  checked :  for  example,  in 
Prob.  1 3,  see  that  AF=  BE  ;  in  Prob.  24,  see  whether  AD  =  CE  =  CB. 

INKING.     Either  of  the  following  systems  may  be  used  :  - 

(a)  All  lines  to  be  in  black.    Given  lines,  dash  and  dot ;  construction  lines,  short 
dashes ;  result  lines,  solid.     (See  Fig.  55.) 

(b)  All  lines  to  be  in  color  and  drawn  full.     Given  lines,  blue ;  construction 
lines,  red ;  result  lines,  black. 

The  French  curve  should  be  used  in  inking  the  irregular  curves. 

(79) 


8o 


GEOMETRICAL  CONSTRUCTION. 


Problem  i.—  To  bisect  a  straight  line  or  a  circu- 
lar arc. 

Let  AB  or  AE'B  be  the  given  line.  With  any 
appropriate  radius,  centers  A  and  B,  describe  arcs  inter- 
secting in  points  C  and  D.  Draw  CD  intersecting  AB 
and  AE' B  in  E  and  E' ',  the  required  middle  points. 

Problem  2. —  To  draw  a  line  perpendicular  to  a 
given  line  at  a  given  point  in  the  line. 

Let  AB  be  the  given  line,  and  C  the  given  point. 
With  any  radius,  C  as  center,  draw  arcs  intersecting 
AB  in  D  and  E.  With  any  appropriate  radius,  centers 
D  and  E,  describe  arcs  intersecting  in  point  F.  Draw 
FC,  the  required  perpendicular. 

Problem  3. —  To  draw  a  perpendicular  to  a  line  at  or 
near  its  extremity.  First  Method. 

Let  AB\>z  the  given  line,  and  A  the  given  point. 
With  any  appropriate  radius,  center  A,  draw  the  arc 
CDE.  With  the  same  radius,  center  E,  intersect  arc 
CDE  in  the  point  D.  With  the  same  radius,  center  D, 
intersect  arc  CDE  in  C.  With  the  same  or  any  appro- 
priate radius,  centers  C  and  D,  draw  arcs  intersecting 
in  F.  Draw  FA,  the  required  perpendicular. 

Problem  4. —  To  draw  a  perpendicular  to  a  line  at  or 
near  its  extremity.  Second  Method. 

Let  AB  be  the  given  line,  and  A  the  given  point. 
Assume  any  point  D.  With  radius  AD,  center  D,  draw 
the  arc  CAB,  intersecting  AB  at  B.  Draw  from  B 
through  point  D,  to  intersect  arc  CAB  in  C.  Draw 
AC,  the  required  perpendicular. 

Problem  5. —  To  draw  a  perpendicular  to  a  line  from 
a  point  outside  the  line. 

Let  AB  be  the  given  line,  and  £Tthe  given  point. 
With  any  appropriate  radius,  center  C,  draw  an  arc 
intersecting  AB  in  points  D  and  E.  With  any  appro- 
priate radius,  centers  D  and  E,  draw  arcs  intersecting  in 
point  F.  Draw  CF,  the  required  perpendicular. 


/\ 


GEOMETRICAL  CONSTRUCTION. 


81 


Problem  6. —  To  draw  a  perpendicular  to  a  given 
line  from  a  point  opposite  to  the  end  of  the  line. 

Let  AB  be  the  given  line,  and  Cthe  given  point. 
Draw  a  line  from  C  to  any  point,  as  B,  in  AB.  Bisect 
CB  at  D  (Prob.  i).  With  CD  as  radius,  center  D, 
draw  arc  CAB,  intersecting  the  given  line  at  A.  Draw 
CA,  the  required  perpendicular. 

Problem  7. —  To  draiv  a  line  at  a  given  distance 
from  and  parallel  to  a  given  line. 

Let  AB  be  the  given  line,  and  CD  the  given  dis- 
tance. With  radius  CD,  any  two  assumed  points  E 
and  F  on  the  line  as  centers,  draw  arcs  GH  and  JK. 
Erect  perpendiculars  to  AB  at  points  E  and  /''(Prob. 
3),  intersecting  arcs  GH  and  JK  in  points  H  and  J. 
Through  points  ffandj  draw  HJ,  the  required  line. 

Problem  8. —  To  draiv  a  line  parallel  to  a  given 
line  and  passing  through  a  given  point. 

Let  AB  be  the  given  line,  and  D  the  given  point. 
With  any  appropriate  radius,  center  D,  draw  arc  EC. 
With  the  same  radius,  center  E,  describe  arc  DF.  With 
chord  DF  as  radius,  center  E,  intersect  arc  CE  in  point 
C.  Draw  CD,  the  required  line. 

Problem  9. —  To  bisect  an  angle. 

Let  JSACbe  the  given  angle.  With  any  appropri- 
ate radius,  center  A,  describe  an  arc  intersecting  AB 
and  A  Cm  points  B  and  C.  With  any  radius,  centers 
B  and  C,  describe  arcs  intersecting  in  point  D.  Draw 
AD,  the  bisector  of  the  given  angle. 

Problem  10. —  To  trisect  a  right  angle. 

Let  ABC  be  the  given  right  angle.  With  any  ap- 
propriate radius,  center  B,  describe  an  arc  intersecting 
AB  and  BC  in  points  A  and  C.  With  the  same  radius, 
centers  A  and  C,  intersect  arc  A  Cm  points  E  and  D. 
Draw  BD  and  BE,  the  trisectors  of  the  given  right 
angle. 


\o 


82 


GEOMETRICAL  CONSTRUCTION. 
To  construct   an   angle   equal    to   a 


Problem  n. 

given  angle. 

Let  CAB  be  the  given  angle.  Draw  A'B'  of  indefi- 
nite length.  With  any  equal  radii,  centers  A  and  A' ' , 
draw  arcs  CB  and  C'B'.  With  the  chord  BC  as  radius, 
center  B',  intersect  arc  B'C'  in  C '.  Draw  A' C'  ;  then 
angle  C'A'B'  is  equal  to  the  given  angle  CAB. 

Problem  12. —  To  divide  a  given  line  into  any  num- 
ber of  equal  parts.  First  Method. 

Let  AB  be  the  given  line,  and  the  required  number 
of  parts  five.  Through  point  A  draw  AC,  making  any 
angle  with  AB.  Draw  BC1 ',  making  angle  ABC'  equal 
to  CAB  (Prob.  n).  Take  any  distance  as  a  unit,  and 
lay  it  off  on  A  C  and  BC'  as  many  times  as  the  required 
number  of  parts  less  one.  Draw  lines  1-4',  2-j' ',  J-2f, 
4-1',  dividing  AB  into  the  required  number  of  equal 
parts. 

Problem  13. —  To  divide  a  given  line  into  any  num- 
ber of  equal  parts.  Second  Method. 

Let  AB  be  the  given  line,  and  the  required  number 
of  parts  five.  Draw  AC,  making  any  angle  with  AB. 
Lay  off  on  AC  any  distance  taken  as  a  unit,  as  many 
times  as  the  required  number  of  parts.  Connect  the 
last  point  of  division,  5,  with  point  B.  Parallel  to  5  B 
draw  lines  through  points  4,  j,  2,  I,  intersecting  AB  in 
points  /,  J',  2',  i',  dividing  AB  into  the  required  num- 
ber of  parts. 

Problem  14. —  To  divide  a  given  line  proportionally 
to  a  given  divided  line.  First  Method. 

Let  AE,  divided  into  the  parts  AB,  BC,  CD,  and 
DEt  be  given,  and  let  FG  be  the  line  required  to  be 
divided  proportionally  to  AE.  Draw  F' G' ,  equal  to  FG, 
parallel  to  AE,  and  at  any  convenient  distance  from  it. 
Draw  AF'  and  EG'  produced  to  intersect  in  point  H. 
Draw  BH,  CH,  and  DH,  intersecting  F'G'  in  points  B1 , 
C't  and  D',  marking  the  required  divisions. 


GEOMETRICAL  CONSTRUCTION. 


Problem  15.  —  To  divide  a  given  line  proportionally 
to  a  given  divided  line.  Second  Method. 

Let  AB,  divided  by  the  points  E,  F,  G,  H,  J,  be 
given,  and  CD  the  line  required  to  be  divided  propor- 
tionally to  AB.  Draw  A  K  at  any  convenient  angle 
with  AB,  and  make  AD'  equal  to  CD.  Draw  BD>  ',  and 
parallel  to  it  draw  EE'  ',  FF  ,  etc.,  giving  the  points  E'  ', 
F',  G',  H'  ,  J'  ,  which  mark  the  required  divisions. 

Problem  16.  —  To  fend  the  distance  which  is  the 
fourth  proportional  to  three  given  distances. 

Let  AB,  CD,  and  EF  be  the  given  distances. 
Draw  GJ  of  indefinite  length,  and  lay  off  GH  equal  to 
AB,  and  HJ  equal  to  EF.  Draw  GL  of  indefinite 
length,  and  making  any  convenient  angle  with  GJ.  On 
GL  lay  off  GK  equal  to  CD,  and  draw  KH.  Through 
J,  and  parallel  to  KH,  draw  LJ  intersecting  GL  in  point 
L.  Distance  KL  is  the  required  fourth  proportional  ; 
that  is,  AB  is  to  CD  as  EFis  to  KL. 

Problem  17.  —  To  find  the  distance  which  is  the 
mean  proportional  between  two  given  distances. 

Let  AB  and  CD  be  the  given  distances.  Draw 
EH  of  indefinite  length,  and  lay  off  EG  equal  to  AB, 
and  GH  equal  to  CD.  Bisect  EH  (Prob.  i)  in  point  F. 
With  radius  EF,  center  F,  draw  the  semicircle  EJH. 
At  point  G  erect  a  perpendicular  to  EH  (Prob.  2),  inter- 
secting the  semicircle  in  point  J.  Distance  JG  is  the 
required  mean  proportional  ;  that  is,  AB  is  to  JG  as  JG 
is  to  CD. 

Problem  18.  —  To  draw  a  circle  through  three  points 
not  in  the  same  straight  line,  or  to  circumscribe  a  circle 
about  a  triangle. 

Let  A,  B,  and  D  be  the  given  points  or  ABD  the 
given  triangle.  Bisect  AB  and  AD  by  lines  EG  and  FH, 
intersecting  in  point  C,  the  center  of  the  required  circle. 

Note.  —  To  find  the  center  of  a  circle,  assume  any 
three  points  in  its  circumference  and  use  the  same 
construction. 


84 


GEOMETRICAL  CONSTRUCTION. 


Problem  19. —  To  draiv  a  circular  arc  through  three 
points  not  in  the  same  straight  line,  when  the  center  is 
not  accessible. 

Let  A,  E,  and  J  be  the  given  points.  Draw  AJ. 
With  AJas  radius,  centers  A  and/,  draw  the  arcs  AMP 
and  RNJ.  Draw  AE  produced  to  intersect  arc  RNJ 
in  point  N,  zndJJE  produced  to  intersect  arc  AMP  in 
M.  Above  and  below  points  M  and  N  lay  off  on  arcs 
AMP  and  RNJ,  with  any  convenient  unit,  equal  spaces  as  M  I,  M  i",  N  /',  A" 
/'",  etc.  Draw  J  I  and  A  /'  intersecting  in  F,  a  point  in  the  required  arc. 
Draw  J  2  and  A  2'  intersecting  in  G,  a  second  point  in  the  required  arc. 
Locate  in  like  manner,  aided  by  inspection  of  the  figure  B,  C,  D,  K,  L,  the  rest  of 
the  points  determining  the  required  arc. 

Problem  20. —  Through  a  given  point  to  draw  a  line 
which  shall  pass  through  the  inaccessible  intersection  of 
two  given  lines. 

Let  AB  and  CD  be  the  given  lines,  P  the  given 
point.  Assume  any  two  points  E  and  E'  on  AB,  and 
any  point  F  on  CD ;  draw  PE,  PF,  and  EF.  Through 
E'  draw  E' F'  parallel  to  EF ' ;  draw  E' P'  parallel  to 
EP,  and  F1  P'  parallel  to  FP,  intersecting  in  point  P' . 
Draw  PP',  the  required  line. 


Problem  21. —  To  construct  a  triangle,  the  lengths 
of  its  three  sides  being  given. 

Let  AB,  CD,  and  EF  be  the  given  sides,  and  AB 
be  the  base.  With  CD  as  radius,  center  A,  describe 
an  arc  at  G.  With  EF  as  radius,  center  B,  intersect 
the  preceding  arc  in  point  G.  Draw  AG  and  GB, 
completing  the  required  triangle  AGB. 

Problem  22. —  To  construct  a  rectangle,  the  lengths 
of  its  sides  being  given. 

Let  AB  and  CD  be  the  given  sides.  At  either  end 
of  AB,  as  A,  draw  a  perpendicular  (Prob.  4)  of  indefinite 
length,  and  upon  it  lay  off  EA  equal  to  CD.  With  AB 
as  radius,  center  E,  describe  an  arc  at  F.  With  CD  as 
radius,  center  B,  intersect  the  preceding  arc  in  point  F.  Draw  EF  and  FB,  com 
pleting  the  required  rectangle. 


GEOMETRICAL  CONSTRUCTION. 


Problem  23. —  To  construct  a  polygon  equal  to  a 
given  irregular  polygon. 

Let  ABCDFE  be  the  given  polygon.  Draw  lines 
dividing  the  given  polygon  into  triangles,  as  ABE,  EEC, 
etc.  Draw  E' F1  equal  to  EF,  and  on  E' F'  construct 
triangle  C' E'F' ,  equal  to  triangle  CEF  (Prob.  21).  On 
E'  C'  construct  triangle  E' B' C' ,  equal  to  triangle  EEC. 
By  similar  construction  draw  the  triangles  E' A' B'  and 
C'D'F' ,  completing  the  required  polygon. 

Problem  24. —  To  construct  a  regular  pentagon,  the 
length  of  one  side  being  given. 

Let  AB  be  the  given  side.  Bisect  AB  by  the  per- 
pendicular FH.  Make  GH  equal  to  GB.  With  radius 
GB,  centers  B  and  H,  draw  arcs  intersecting  at  J. 
Draw  AJ  produced,  and  make  JK  equal  to  GB.  With 
radius  KB,  center  B,  intersect  FH  at  F;  with  the  same 
radius,  center  F,  draw  the  circle  ABD.  With  AB  as 
radius,  start  at  A,  and  cut  the  circle  in  points  C,  D,  and 
E.  Draw  AC,  CD,  DE,  and  EB,  completing  the  re- 
quired pentagon. 


Problem  25. —  To  construct  a  regular  hexagon,  the 
lengtJi  of  one  side  being  given. 

Let  AB  be  the  given  side.  With  radius  AB,  centers 
A  and  B,  describe  arcs  intersecting  in  point  C.  With 
radius  AB,  center  C,  draw  the  circle  AEB.  With  the  same 
radius,  starting  at  point  A,  cut  the  circle  in  points  D,  E,  F, 
G,  locating  the  remaining  sides  of  the  required  hexagon. 

Problem  26. —  To  construct  a  regular  pentagon,  the 
circumscribing  circle  being  given. 

Let  AEB  be  the  given  circle.  Draw  any  diameter, 
AB,  of  the  circle,  and  at  its  center,  C,  draw  EC  perpen- 
dicular to  AB.  Bisect  CB  in  K,  and  with  EK  as  radius, 
center  K,  draw  arc  EJ.  With  chord  JE  as  radius,  center 
E,  intersect  the  given  circle  in  D.  DE  is  one  side  of  the 
required  pentagon. 


86 


GEOMETRICAL  CONSTRUCTION. 


Problem  27. —  To  construct  a  regiilar  polygon  of  any 
number  of  sides,  the  length  of  one  side  being  given. 

Let  AB  be  the  given  side,  and  the  number  of  sides 
seven.  With  radius  AB,  A  as  center,  draw  the  semi- 
circle I—4-—B.  Divide  the  semicircle  into  as  many  equal 
parts  as  there  are  sides  in  the  required  polygon.  Draw 
AD,  which  is  a  side  of  the  required  polygon,  connecting 
point  A  with  the  second  point  of  division  in  the  semi- 
circle. Bisect  AB  and  AD  (Prob.  i),  and  produce  the 
bisectors  to  intersect  in  point  C,  the  center  of  the  required  polygon.  With  radius 
AC,  center  C,  draw  the  circle  AFH.  With  AB  as  radius,  start  at  D,  and  cut  the 
circle  in  points  E,  F,  G,  and  H,  the  remaining  corners  of  the  polygon. 

Problem  28. —  To  find  the  point  of  tangency  of  a 
straight  line  and  a  circle. 

Let  AB  be  the  given  straight  line,  and  DF  the 
given  circle,  described  from  C.  From  C  draw  CE  per- 
pendicular to  AB  (Prob.  6),  intersecting  AB  at  E, 
the  required  point  of  tangency. 

Problem  29. —  To  draw  a  circular  arc  tangent  to  a 
straight  line  and  to  a  circle  at  a  given  point. 

Let  AB  be  the  given  straight  line  and  E  the  given 
point  on  circle  DE  described  from  point  C.  Draw  CE 
produced.  Draw  EF  perpendicular  to  CE  (Prob.  2). 
Bisect  angle  EFA  (Prob.  9).  Point  G,  the  intersection 
of  the  bisector  and  of  CE  produced,  is  the  center  of  the 
required  arc. 

Problem  30. —  To  connect  two  given  lines  by  a  re- 
versed curve,  given  one  point  of  tangency  and  the  radii 
of  the  two  curves. 

Let  AB  and  CD  be  the  given  lines,  and  B  the 
given  point  of  tangency.  At  B  draw;  the  indefinite  line 
EF  perpendicular  to  AB  (Prob.  4) .  Make  BE  equal  to  one  given  radius,  and  BF 
equal  to  the  other  given  radius.  Draw  the  indefinite  line  HJ  parallel  to  CD  and  at 
a  distance  equal  to  EB  from  CD  (Prob.  7).  With  radius  EF,  center  F,  draw  arc 
EJ  to  intersect  HJ  in  point  J.  From  J  draw  JC  perpendicular  to  CD,  intersecting 
CD  at  C.  With  radius  BF,  center  F,  draw  arc  BK.  With  radius  CJ,  center  J, 
draw  arc  KC.  BKC  is  the  required  curve. 


GEOMETRICAL  CONSTRUCTION. 


87 


Problem  31. —  To  connect  two  given  parallel  lines 
by  a  reversed  curve,  given  one  point  of  tangency  and  the 
point  of  reversed  curvature. 

Let  AB  and  CD  be  the  given  lines,  A  the  given 
point  of  tangency,  and  K  the  given  point  of  reversed  c  — 6 
curvature.  Draw  AK  produced  to  meet  CD  at  D.  At  points  A  and  D,  draw  the 
indefinite  lines  AE  and  DF,  perpendicular  to  AB  and  CD.  Bisect  A  K  and  pro- 
duce the  bisector  to  meet  AE  at  E.  Bisect  KD  and  produce  the  bisector  to  meet 
DFat  F.  With  radius  AE,  center  E,  draw  arc  AK.  With  radius  DF,  center  F, 
draw  arc  KD.  AKD  is  the  required  curve. 

Problem  32. —  To  connect  two  given  parallel  lines 
by  a  reversed  curve,  given  the  points  of  tangency  and  the 
ratio  of  the  radii. 

Let  AB  and  CD  be  the  given  parallel  lines,  B  and 
C  the  given  points  of  tangency,  and  let  the  required 
radii  be  in  the  ratio  of  HJ  to  JK.  At  the  points  of 
tangency  B  and  C,  draw  the  indefinite  lines  BE  and  CF,  perpendicular  to  the  given 
lines.  Connect  B  and  C  and  find  point  G,  so  that  BG  is  to  GC  as  HJ  is  to  JK 
(Prob.  15).  Bisect  BG  and  produce  the  bisector  to  meet  BE  at  E.  Bisect  GC 
and  produce  the  bisector  to  meet  CF  at  F.  With  radius  BE,  center  E,  draw  arc 
BG.  With  radius  CF,  center  F,  draw  arc  CG.  BGC'is  the  required  curve. 

Problem  33. —  To  connect  two  given  non-parallel 
lines  by  a  reversed  curve,  given  the  points  of  tangency 
and  the  ratio  of  the  radii. 

Let  AB  and  CD  be  the  given  lines,  B  and  C  the  given 
points  of  tangency.  At  points  B  and  C,  draw  the  indefi- 
nite lines  BE  and  CF,  perpendicular  to  AB  and  CD. 
Connect  B  and  C.  Bisect  BC  at  G  and  with  radius 
BG,  center  G,  draw  the  indefinite  arc  BH.  On  BC  find  point  J,  so  that  the  ratio 
of  ZT/toyCis  the  given  ratio  of  the  radii  (Prob.  15).  From  J  draw  JK  perpen- 
dicular to  AB,  andyZ,  perpendicular  to  CD.  Make  LM  equal  to  B  K.  With  radius 
MC,  center  C,  describe  an  arc  intersecting  arc  BH  in  H.  Draw  BH  of  indefinite 
length,  and  make  BP  equal  to  BC.  From  P  draw  PQ  perpendicular  to  CD,  make 
PQ  equal  to  CJ,  and  draw  BQ.  From  C  draw  ££"  parallel  to  BQ,  intersecting  BE 
in  E.  From  .£  draw  ZTjF  parallel  to  BP,  intersecting  CF  at  F.  With  radius  Z?.Zi, 
center  E,  draw  arc  .Z?Af.  With  radius  CF,  center  F,  draw  arc  NC.  BNC  is  the 
required  curve. 


88 


GEOMETRICAL  CONSTRUCTION. 


Problem  34. —  To  draw  a  circle  tangent  to 
two  given  circles  and  at  a  given  point  in  one  of 
them  (tzvo  solutions).  First  Method. 

Let  ABD  and  EFH  be  the  given  circles, 
and  B  the  given  point.  Draw  from  point  B 
through  C,  the  center  of  circle  ABD,  and  pro- 
duce the  line  indefinitely. 

First  solution.  Make  BJ  equal  to  the 
radius  of  circle  EFH.  Draw  JG,  bisect  it,  and 
produce  the  bisector  to  intersect  CB  produced 
in  point  L.  With  BL  as  radius,  center  L,  draw 
arc  BO  of  the  required  circle. 

Second  solution.  Make  BM  equal  to  the 
radius  of  circle  EFH.  Draw  MG,  bisect  it,  and 
produce  the  bisector  to  intersect  CL  in  N. 
With  BN  as  radius,  center  N,  draw  BP,  the  re- 
quired circle. 


Problem  35. —  To  draw  a  circle  tangent  to 
two  given  circles  and  at  a  given  point  in  one  of 
them  (two  solutions] .  Second  Method. 

Let  ABD  and  MEJ  be  the  given  circles, 
and  B  the  given  point.  Draw  from  point  B 
through  C,  the  center  of  circle  ABD,  and  pro- 
duce the  line  indefinitely.  Through  G,  the  cen- 
ter of  circle  MEJ,  draw  a  line  parallel  to  BC, 
cutting  the  circle  MEJ  in  points  E  and  F. 

First  solution.  Draw  BE  produced  to  meet 
the  circle  MEJ  in  point  J.  Draw  JG  produced 
to  meet  BC  at  L.  With  BL  as  radius,  center 
L,  draw  arc  BOJ  oi  the  required  circle. 

Second  solution.  Draw  BF  intersecting 
circle  MEJ  in  point  M.  Draw  GM  produced 
to  meet  BC  at  N.  With  BN  as  radius,  center 
N,  draw  BMP,  the  required  circle. 


F\ 


89 


GEOMETRICAL  CONSTRUCTION. 

Problem  36. —  To  inscribe  a  circle  within  a  triangle. 

Let  ABD  be  the  given  triangle.  Bisect  any  two 
angles  of  the  triangle  (Prob.  9) .  The  intersection  C  of 
the  bisectors  is  the  center  of  the  required  circle. 

Note. —  If  adjacent  exterior  angles,  as  EAB  and 
ABF,  be  bisected,  the  bisectors  will  intersect  in  a  point, 
C',  which  is  the  center  of  a  circular  arc  tangent  to  one 
side  of  the  triangle  and  to  two  of  its  sides  produced. 

Problem  37. —  Witliin  an  equilateral  triangle  to  in- 
scribe three  equal  circles,  each  tangent  to  the  otliers  and 
to  two  sides  of  the  triangle, 

Let  ABC  be  the  given  equilateral  triangle.  Bisect 
the  sides  in  points  D,  E,  and  F.  Draw  FA,  DC,  and 
BE.  With  radius  DE,  centers  D,  E,  and  F,  draw  arcs 
EF,  FD,  and  DE.  The  intersections  G,  J,  and  H  are 
the  centers  of  the  required  circles. 

Problem  38. —  Within  an  equilateral  triangle  to 
inscribe  six  equal  circles,  tangent  to  each  other. 

Let  ABC  be  the  given  equilateral  triangle.  Bisect 
the  sides  in  points  D,  E,  and  F.  Draw  BE,  DC,  and 
FA.  Bisect  the  angle  EBC  by  line  BG,  intersecting  AF 
in  point  G.  Make  DJ  and  EK  each  equal  to  FG,  and 
through  points  /,  K,  and  G,  draw  L M,  LH,  and  HM, 
parallel  to  the  sides  BC,  BA,  and  AC  of  the  triangle. 
With  GF  as  radius,  centers  L,J,  H,  K,  M,  and  G,  de- 
scribe the  required  circles. 

Problem  39. —  Within  a  given  circle  to  inscribe 
three  equal  circles  tangent  to  each  other. 

Let  BDG  be  the  given  circle,  center  C.  Divide 
the  circumference  into  six  equal  parts  by  making  the 
chords  AD,  DF,  etc.,  each  equal  to  the  radius  CA  of  the 
circle.  Draw  the  diameters  AG,  BF,  and  ED.  Pro- 
duce any  diameter,  as  BF,  and  make  FH  equal  to  CF. 
Draw  GH  and  bisect  the  angle  CHG  by  the  line  HJ,  in- 
tersecting CG  in  point  /.  With  radius  JC,  center  C,  draw  the  circle  MKL, 
intersecting  the  diameters  in  points  M,  K,  and  L,  the  centers  of  the  required 
circles. 


9o 


GEOMETRICAL  CONSTRUCTION. 


Problem  40. —  Within  a  given  circle  to  inscribe  any 
given  number  of  equal  circles  tangent  to  each  other. 

Let  DAE  be  the  given  circle,  and  the  required 
number  of  inscribed  circles  five.  Divide  the  circle  DAE 
into  ten  equal  parts  (Prob.  26),  and  draw  the  diameters 
AB,  DE,  etc.  At  the  extremity  of  any  diameter,  as  B, 
draw  the  tangent  FG  perpendicular  to  AB,  and  produce 
the  adjacent  diameters  to  intersect  the  tangent  at  Fand 
G.  In  the  triangle  CFG  find  the  center  H  of  the 
inscribed  circle  (Prob.  36).  With  radius  HC,  center  C, 
giving  the  remaining  required  centers,  L,  J,  K,  and  M. 


draw  the  circle  LJK, 


Problem  41. —  7!?  draw  an  ellipse, 
given  the  rectangular  axes.  First  MetJi- 
od. 

Let  AB  be  the  major  axis,  and  DE  the 
minor  axis.  With  radius  equal  to  one-half 
the  major  axis,  centers  D  and  E,  intersect 
AB  in.  points  F  and  F' ',  the  foci  of  the 
required  curve.  Divide  by  eye,  FC  and  CF'  into  any  number  of  parts,  decreasing 
from  Cto  Fand  from  Cto  F' .  To  locate  the  points  of  the  curve  :  With  A$  as  radius, 
center  F,  describe  an  arc  at  L.  With  B$  as  radius,  center  F ,  intersect  the  pre- 
ceding arc  in  L,  a  point  in  the  required  curve.  With  radii  A$,  Aj,  A2,and  Ai, 
center  F,  describe  arcs  at  K,  /,  H,  and  G.  With  radii  Bj,  £j,  B2,  and  Bl,  center 
F',  intersect  in  the  same  order  the  arcs  at  Kt  J,  H,  and  G,  four  additional  points 
in  the  required  curve.  Repeat  in  each  of  the  remaining  quadrants. 

Problem  42. —  To  draw  a  tangent  to  an  ellipse  at  a  given  point  in  the  curve. 
First  Method. 

Let  Q  be  the  given  point.  Find  the  foci  F  and  F'  (Prob.  41).  Draw  F'Q 
and  FQ  produced.  Bisect  angle  F1 QR  (Prob.  9).  The  bisector  ST  is  the  required 
tangent. 

=» 
Problem  43. —  To  draw  a  tangent  to  an  ellipse  from  a  given  point  outside  the 

curve.     First  Method. 

Let  J/be  the  given  point.  Find  the  foci  F  and  F'  (Prob.  41).  With  FJ/as 
radius,  center  M,  draw  arc  FN.  With  AB  as  radius,  center  F',  intersect  arc  FN 
in  point  N.  Draw  NF1 .  Bisect  the  angle  FMN  (Prob.  9)  and  draw  the  bisector, 
intersecting  F'TVat  P.  MP  is  tangent  to  the  ellipse  at  point  P. 


GEOMETRICAL  CONSTRUCTION. 


Problem  44. — To  draw  an  ellipse,  given 
the  rectangular  axes.  Second  Method. 

Let  AB  and  DE  be  the  axes.  With 
A  C  and  DC  as  radii,  center  C,  describe  the 
major  and  minor  auxiliary  circles  AGQ  and 
DJ' E.  Assume  points  in  the  outer  circle, 
as  G,  H,J.  Draw  radii  CG,  CH,  and  CJ. 
Draw  lines  parallel  to  AB  from  points  Gf, 
H',  and  J' ,  intersected  by  lines  parallel  to 
DC  from  G,  H,  and  /  in  £",  H",  and  /", 
points  in  the  required  curve.  Repeat  in  each  of  the  remaining  quadrants. 

Problem  45. —  71?  draw  a  tangent  to  an  ellipse  at  a  given  point  in  the  curve. 
Second  Method. 

Let  K  be  the  given  point  on  the  ellipse.  At  K1 ',  the  corresponding  point  on 
the  major  auxiliary  circle  (see  Prob.  44),  draw  the  tangent  LK1 ',  perpendicular  to 
the  radius  K'  C,  meeting  the  major  axis  at  L.  Draw  LK,  the  required  tangent. 

Note. —  The  minor  auxiliary  circle  and  minor  axis  may  be  similarly  used. 

Problem  46. —  7<?  draw  a  tangent  to  an  ellipse  from  a  given  point  outside  the 
curve.  Second  Method. 

Let  M  be  the  given  point.  Find  either  focus,  as  F  (Prob.  41).  On  MF  as 
diameter,  draw  a  circle  intersecting  the  major  auxiliary  circle  in  points  TV  and  O, 
through  which  draw  MN  and  MO,  the  required  tangents. 

To  find  the  exact  point  of  tangency,  as  of  MP.  Take  the  point  P  where  the 
tangent  MO  intersects  the  major  axis.  On  CP  as  diameter  draw  a  semicircle, 
intersecting  the  major  auxiliary  circle  at  Q.  Find  Q" ,  the  point  on  the  ellipse 
corresponding  to  Q  (Prob.  44).  Point  Q"  is  the  point  of  tangency. 

Note. —  The  minor  axis  and  minor  auxiliary  circle  may  be  similarly  used. 

Problem  47. —  To  draw  an  ellipse, 
given  the  oblique  axes. 

Let  AB  be  the  major  axis,  and  DE 
the  minor  axis.  Through  point  E  draw 
HJ  parallel  to  AB,  and  through  point  A, 
HF  parallel  to  ED  ;  complete  the  parallelogram  HFGJ,  containing  the  points  D  and 
B.  Divide  CB  and  GB  into  any  number  of  similarly  spaced  parts,  as  shown  by 
/,  2,  3,  and  /',  2',  3'.  Draw  Dl' ,  D2' ,  Df,  and  El,  E2,  Ej  produced.  The 
intersections  K,  L,  and  M,  are  points  in  the  required  curve. 

Note. —  The  same  construction  applies  when  the  axes  are  at  right  angles. 


GEOMETRICAL    CONSTRUCTION. 


Problem  48. —  To  find  the  axes  of  symmetry 
(rectangular  axes]  of  an  ellipse. 

Let  AC  and  CB  be  the  oblique  semi-axes. 
Draw  AD  perpendicular  to  CB,  and  make  AD 
and  AE  each  equal  to  CB.  Draw  DC  and 
CE,  and  produce  both  indefinitely.  Bisect  the 
angles  DCE  and  ECF;  the  bisectors  CM  and 
CP  are  the  major  and  minor  axes  respectively. 

To  find  the  extremities  of  the  rectangular 
axes.  Make  CX  and  CY  each  equal  to  CE. 
Bisect  Z>Fand  lay  off  CL  and  CM,  each  equal 
to  one-half  of  DY ;  bisect  DX  and  lay  off  CN 
and  CP,  each  equal  to  one-half  of  DX.  Points 
L,  M,  N,  and  P  are  the  extremities  of  the  rec- 
tangular axes. 

Problem  49. —  To  draw  a  parabola,  given 
the  focus  and  the  directrix. 

Let  AR'  be  the  directrix  of  the  parabola, 
BC  its  axis,  and  F  the  focus.  Bisect  BF  in 
point  Z>,  the  vertex  of  the  parabola.  Assume 
on  the  axis  BC,  any  points,  as  G,  H,  .  .  .  M,  and 
through  these  points  draw  the  indefinite  lines 
G'G",  H'H",  etc.,  parallel  to  AR' .  With  BG 
as  radius,  center  F,  intersect  G'G"  in  points  G' 
and  G" ;  with  radius  BH,  center  F,  intersect 
H'H"  in  H'  and  H" ',  and  so  on. 


First 


Problem  50. —  71?  draw  a  tangent  at  a  given  point  on  a  parabola. 
Method. 

Let  L'  be  the  given  point.  Draw  from  L'  to  the  focus  F.  Through  L'  draw 
L'N  parallel  to  BC.  Bisect  the  angle  JVL'Fby  L'O,  the  required  tangent. 

Problem  51. —  To  draw  a  tangent  to  a  parabola  from  a  given  point  outside  the 
curve.  First  Method. 

Let  P  be  the  given  point.  Connect  P  with  the  focus  F.  With  FP  as  radius, 
center  P,  draw  an  arc  intersecting  the  directrix  AR'  in  points  R  and  R' .  Bisect 
the  angles  RPF&nd  FPR'  ;  the  bisectors  PS  and  PS'  are  the  required  tangents. 

To  find  the  exact  points  of  tangency.  From  R  and  R'  draw  lines  parallel  to 
BC,  intersecting  the  tangents  PS  and  PS'  in  5  and  S' ,  the  required  points. 


GEOMETRICAL  CONSTRUCTION. 


93 


Problem  52. — To  draw  a  parabola, 
given  the  axis,  the  vertex,  and  a  point  on 
the  curve. 

Let  AB  be  the  axis  of  the  parabola, 
A  its  vertex,  and  D  a  point  on  the  curve. 
Complete  the  rectangle  ABDC.  Divide 
AC  into  any  number  of  equal  parts,  say 
five,  by  points  /,  2,  J,  4.  Divide  CD  into 
the  same  number  of  equal  parts  by  points 
i',  2',  3',  4' .  Through  points  /,  2,  J,  4, 
draw  lines  parallel  to  AB.  Draw  Al' ,  A2', 
Aj',  A 4',  intersecting  the  parallels  from 
/,  2,  3,  4,  in  G,  H,J,  K,  points  in  the  required  curve. 
ABD'O. 

To  find  the  focus.     From  point  7  draw  a  line  perpendicular  to  A  4' 
produced  to  intersect  the  axis  AB  in  F,  the  required  point. 

Problem  53. —  To  drazv  a  tangent  at  a  given  point  on  a  parabola.  Second 
Method. 

Let  D  be  the  given  point.  Draw  CD  parallel  to  AB,  intersecting  AC  in  point 
C.  Bisect  AC  in.  point  L.  Draw  LD,  the  required  tangent. 

Problem  54. —  To  draw  a  tangent  to  a  parabola  from  a  given  point  outside  the 
curve.  Second  Method. 

Let  .A^be  the  given  point.  Connect  TV  with  the  focus  .F(Prob.  52).  On  NF 
as  diameter  draw  a  circle  intersecting  CC'  in  points  O  and  O' .  Through  O  and 
O'  draw  NP  and  NP' ,  the  required  tangents. 

To  find  the  exact  point  of  tangency.  Make  O' T  equal  to  O'  A .  Through  T 
draw  TP'  parallel  to  AB,  intersecting  NP'  in  P' ,  the  required  point  of  tangency. 

Problem  55. — To  dra^v  a  hyperbola, 
given  tJie  major  axis  and  one  point  on  the 
curve. 

Let  AB  be  the  major  axis,  and  D  the 
given  point.  Draw  the  rectangle  BCDE. 
Divide  CD  and  ED  each  into  any  number 
of  equal  parts,  in  this  case  four.  Draw  Bl, 
B2,  B$,  and  Al' ,  A21 ,  Ajf,  intersecting  in 
F,  G,  and  H,  points  in  the  required  curve.  Draw  the  rest  of  this  branch  and  the 
opposite  branch  of  the  curve  by  the  same  construction. 


94 


GEOMETRICAL  CONSTRUCTION. 


Problem  56. —  To  find  the  asymptotes 
and  foci  of  a  Jiyperbola. 

Let  AB\>z  the  major  axis  of  the  hy- 
perbola, and  G  a  known  point  on  the  curve. 
Bisect  AB  by  the  perpendicular  DH  (Prob. 
i).  With  radius  AC,  center  C,  draw  the 
circle  ABH. 

To  find  the  asymptotes.  At  H  draw 
the  tangent  HJ  parallel  to  AB.  Through 
the  known  point  of  the  curve,  G,  draw  DG  parallel  to  AB.  With  DG  as  radius, 
center  C,  draw  an  arc  intersecting  HJ  in  point  J.  Make  DE  equal  to  HJ  and 
draw  CE,  one  required  asymptote.  Make  angle  KCL  equal  to  angle  LCM 
(Prob.  1 1),  and  draw  KC,  the  other  required  asymptote. 

To  find  the  foci.  At  the  points  of  intersection,  TV  and  N',  of  ME  with  the 
circle  ABH,  draw  NF  and  N' F'  perpendicular  to  ME,  intersecting  the  major 
axis  AB  in  points  /''and  F',  the  required  foci. 

Note. — The  circle  ABH'vs>  known  as  the  major  auxiliary  circle. 


Problem  57. — To  draw  a  tangent  to 
a  hyperbola  at  a  given  point  in  the  curve. 

Let  D  be  the  given  point.  Draw  the 
major  auxiliary  circle  on  AB  as  diameter. 
From  D  draw  DE  perpendicular  to  AB 
(Prob.  5).  On  EC  as  diameter,  draw  the 
semicircle  EGC,  intersecting  the  major 
auxiliary  circle  in  point  G.  From  G  draw 
GH  perpendicular  to  AB.  Draw  DH,  the 
required  tangent. 


Problem  58. —  To  draiu  a  tangent  to  a  hyperbola  from  a  given  point  outside 
the  curve. 

Let  /  be  the  given  point.  Connect  /  with  either  focus,  as  F' .  On  JF'  as 
diameter,  draw  a  circle  intersecting  the  major  auxiliary  circle  at  points  K  and 
K' .  Draw  KJzn&JK',  the  required  tangents. 

To  find  the  exact  point  of  tangency.  Tangent  JK'  intersects  the  major  axis 
AB  in  point  L.  At  L  draw  LM  perpendicular  to  AB  and  intersecting  the  major 
auxiliary  circle  at  M.  Draw  CM,  and  perpendicular  to  CM  draw  MN.  Draw  NO 
perpendicular  to  AB,  intersecting  the  tangent  JK'  in  point  O,  the  required  point 
of  tangency. 


GEOMETRICAL  CONSTRUCTION. 


Problem  59. —  To  draw  an  ellipse  with  a 
trammel,  given  the  rectangular  axes. 

Let  AB  and  CD  be  the  given  axes.  On 
the  edge  of  a  strip  of  paper  or  cardboard,  mark 
the  distance  A' E'  equal  to  the  semi-major  axis 
AE.  Mark  the  distance  E' F  equal  to  the 
semi-minor  axis  CE.  Place  the  trammel  so  that 
point  A'  falls  on  the  axis  CD,  produced  if 
necessary,  and  point  F  on  the  axis  AB ;  then 
point  E'  will  be  a  point  of  the  required  ellipse. 
Find  as  many  points  as  desired,  and  draw  the 
curve. 

Problem  60. —  To  draw  a  curve  approximat- 
ing an  ellipse,  composed  of  circular  arcs,  given 
the  major  axis. 

Let  AB  be  the  given  major  axis.  Make 
AC  and  C'B  each  equal  to  five-sixteenths  of  AB 
(Prob.  15).  With  AC  as  radius,  centers  £7 and 
O ',  draw  the  circles  ADE'  and  DBF',  intersect- 
ing in  D  and  D' .  Draw  DC,  DC',  D' C,  and 
D'C,  all  produced.  With  radius  E' D,  centers 
D  and  D1,  draw  arcs  E'F'  and  EF,  completing 
the  required  curve. 

Note. —  The  minor  axis  of  this  curve  is  three- 
quarters  of  the  major  axis. 

Problem  61. —  To  draw  a  curve  approximat- 
ing an  ellipse,  composed  of  circular  arcs,  given 
the  major  and  minor  axes.  First  Method. 

Let  AB  be  the  major  axis  and  DE  the 
minor  axis.  Draw  DB.  Make  CG  equal  to  CD 
and  make  DH  equal  to  GB.  Bisect  HB  by  line 
f  K,  intersecting  CB  in  L' ' ,  and  CE  produced  in 
J' .  Make  CJ  equal  to  CJ' ,  and  CL  equal  to 
CL' .  Draw  J' L,  JL' ,  and  JL,  all  produced. 
To  draw  the  curve :  With  radius  f  D,  centers 
/'  and  /,  draw  the  arcs  MDN  and  M' EN' . 
With  radius  LA,  centers  L  and  L',  draw  the 
arcs  MAM'  and  NBN' . 


95 


96 


GEOMETRICAL  CONSTRUCTION. 


Problem  62. —  To  draiv  a  curve  ap- 
proximating an  ellipse,  composed  of  circu- 
lar arcs,  given  the  major  and  minor 
axes.  Second  Method. 

Let  AB  be  the  major  axis,  and  DE 
the  minor  axis.  Produce  DE  indefi- 
nitely in  both  directions.  Through  E, 
draw  HJ  parallel  to  AB,  and  complete 
the  rectangle  HFGJ,  its  sides  pass- 
ing through  points  A,  D,  and  B.  Draw 
AD.  From  point  jpdraw  a  perpendicular 
to  AD  (Prob.  5),  intersecting  AB  in  Z 
and  produced  to  intersect  DE  produced 
in  K' .  Make  CK  equal  to  CK' ,  and 
CL'  equal  to  CL.  With  radius  DC, 
center  C,  draw  an  arc  intersecting  AB 
in  point  N.  On  AN  as  a  diameter  draw  the  semicircle  AMN.  Make  CO  and  CO' 
each  equal  to  MD,  and  with  radius  OK,  centers  K  and  K' ,  draw  arcs  through 
points  O  and  O' .  Make  ^/^  and  P',5  each  equal  to  MC,  and  with  radius  LP, 
centers  Z  and  Z',  intersect  the  arcs  drawn  through  O  and  0'  in  points  Q,  Q', 
R,  and  R' .  Draw,  of  indefinite  length,  LQ,  LR,  L' Q' ,  and  L' R' .  Draw,  of 
indefinite  length,  K' R,  K'R',  KQ,  and  KQ'.  To  draw  the  required  curve: 
With  radius  DK' ,  centers  K1  and  K,  describe  arcs  SDTand  S'ET'.  With  radius 
SR,  centers  R,  R' ,  Q,  and  Q ',  draw  arcs  S£/,  S'U't  TV,  and  T'  F'.  With  radius 
AL,  centers  Z  and  Z',  draw  arcs  UAU'  and  VBV . 

Problem  63. —  To  draiv  an  oval,  given  its  width. 

Let  AB  be  the  width  of  the  oval.  On  AB  as  di- 
ameter draw  the  circle  AEB.  With  radius  AB,  centers 
A  and  B,  draw  arcs  intersecting  in  D.  Draw  DC. 
Bisect  arcs  AE  and  EB  in  points  Fand  F' .  Draw  ^l/7' 
and  BF  produced  to  intersect  arcs  AGD  and  DG'B  in 
£  and  G' .  Bisect  AC  and  CB  in  Zf  and  ZT.  Draw 
HD  and  //'Z>,  intersecting  ^4G'  and  GZ?  in  Z  and  Z'. 
Bisect  *jy  in  K  and  draw  ZAT  and  L' K  produced. 
With  raums  GZ',  centers  L'  and  Z,  draw  arcs  GM  and 
J/'G'.  Bisect  HC and  £#'  in  ^V and  N' .  Draw  A^Z>  and 
N'D,  intersecting  LM'  and  J/Z'  in  O  and  <9'.  Draw 

and  O' E  produced.     With  radius  MO' ,  centers  O'  and  O,  draw  arcs  MP  and 
!/'.     With  radius  EP,  center  E,  draw  arc  PP' ,  completing  the  required  curve. 


GEOMETRICAL  CONSTRUCTION. 


97 


Problem  64. —  Given  the  short  diameter,  to  draw 
an  oval  the  long  diameter  of  which  shall  be  iy2  times 
the  short  diameter. 

Let  AB  represent  the  short  diameter.  Bisect 
AB  and  draw  the  perpendicular  DE  produced. 
With  center  C,  draw  the  circle  ADE.  Produce  AB 
in  each  direction,  and  make  AF,  BF' ',  and  EG,  each 
equal  to  AC.  Bisect  EG  in  H.  Draw  /7/and  F'H 
produced.  With  radius  FB,  centers  Fand  F',  draw 
arcs  BJ'  and  AJ.  With  radius  GH,  center  H,  draw  arc  JGJ1 ',  completing  the 
required  curve  ADBJ'GJ. 

Problem  65. —  To   draw  a  variable 
spiral. 

Let  CD  be  the  measure  of  the  re- 
quired curve.  Divide  CD  into  eight 
equal  parts,  as  indicated  by  the  points  /, 
2,  . . .  /.  Upon  division  4-$  as  diameter 
draw  a  circle,  the  eye  of  the  spiral. 
(See  also  the  enlargement,  Fig.  /?.)  On 
4-5  as  a  diagonal  draw  the  square  E^F^, 
its  diameters  GK  and  JHt  and  the 
square  GHKJ.  Divide  GL  into  two 
equal  parts,  and  through  the  point  of 
division  draw  $ 4' .  Divide  LM  into  six 
equal  parts,  and  through  the  points  of 
division  draw  8'f ,  4' 3' ,  i'  2' ,  and  $6'. 
Divide  MK  into  tJiree  equal  parts,  and 
through  the  points  of  division  draw  3' 2' 
and  f  6' .  To  draw  the  curve  :  With  4-1' 
as  radius,  center  /',  draw  the  arc  ^N, 
carried  to  the  line  2' l'  produced.  With 
radius  N2r ,  center  2' ' ,  draw  the  arc  from 
point  N  to  O,  lying  in  3' 21  produced. 
With  radius  Ojf,  center  J',  carry  the  arc 
to  4 '3'  produced,  and  so  on.  Take  for 
successive  centers  the  points  4* ',  $',  6' , 
/,  8',J,  K,  H,  and  G,  and  draw  the  arc 
described  from  each  center  to  the  line  drawn  through  the  center  used  and  the 
next  one  in  advance. 


98 


GEOMETRICAL  CONSTRUCTION. 


Problem  66. —  To  draw  an  Ionic 
volute. 

Let  AB,  Fig.  A,  be  the  measure 
of  the  required  curve.  Divide  AB  into 
seven  equal  parts.  Through  the  fourth 
point  of  division  from  A  draw  CD,  in- 
definite in  length  and  perpendicular  to 
AB.  Take  for  the  center  of  the  spiral 
any  point  on  CD,  and  from  this  point, 
with  radius  equal  to  one-half  of  a  division 
of  AB,  describe  circle  FGHJ,  the  eye  of 
the  volute.  (See  also  its  enlargement, 
Fig.  B.}  Draw  the  diameter  of  the  eye, 
GJ,  perpendicular  to  FH.  On  Fffas  a 
diagonal  draw  the  square  FGHJ,  its 
diameters  KNand  ML,  and  the  square 
KLNM.  Divide  KM  into  six  equal 
parts.  Draw  l"2"  parallel  to  and  dis- 
tant from  FH  one-half  of  3' 4'.  Draw 
9"IO"  parallel  to  and  distant  from  MN 
one-half  of  5' ' M.  Project  points  /'  and 
2'  to  GO,  and  through  the  points  thus 
obtained  draw  8"f  and  /'j"  parallel  to 
KL.  Draw  $"6"  parallel  to  and  mid- 
way between  i"2"  and  (}"lo".  Draw 
8' '0",  4" 5",  3" 2",  and  7" 6"  parallel  to 

KM  and  separated  by  spaces  each  equal  to  a  division  of  KM.  To  draw  the  outer 
spiral  TUV  (Fig.  A)  :  Take  Gl"  as  radius,  center  /",  and  draw  arc  GE 
tangent  to  the  eye  of  the  volute  at  G,  and  carried  to  the  line  2" l"  produced. 
With  radius  £2" ',  center  2" ,  draw  from  E  to  Q,  lying  in  3" '2"  produced.  With 
radius  <2j"»  center  j",  describe  an  arc  from  Q  to  4" 3"  produced,  and  so  on.  Take 
for  successive  centers  the  points  4"5"6"f'8"c)"lO",  L,  and  K,  and  draw  the  arc 
described  from  each  center  to  a  line  drawn  through  the  center  used  and  the  next 
one  in  advance.  To  draw  the  inner  spiral  WXY  (Fig.  A)  :  Locate  the  point  P  in 
OH,  midway  between  point  O  and  line  3"  2" .  Locate  the  point  5  midway  between 
P  and  2" .  With  radius  FS,  center  S,  draw  an  arc  from  F  to  Z,  lying  in  3" 2" 
produced.  Locate  point  R,  making,  by  eye,  distance  3"  R  equal  to  2"  S.  With 
radius  ZR,  center  R,  draw  an  arc  from  Z  to  Z' ',  lying  in  4" 3"  produced.  The 
dot  placed  between  4"  and  O  indicates  the  next  center,  and  is  placed  a  distance 
from  4"  equal  to  3"  R.  Continue  in  like  manner. 


GEOMETRICAL  CONSTRUCTION.  oo 

Problem  67. —  To  draw  an  Archimedean 
spiral. 

Let  AN  be  the  measure  of  the  spiral. 
With  NA  as  radius,  center  A,  describe  the 
circle  ^Njf.  Divide  line  AN  and  the  circle 
y 'Nf'  into  the  same  number  of  equal  parts,  as 
twelve.  Draw  Ai' ,  A21 ,  .  .  .  An'.  With  A  as 
center,  draw  arcs  from  each  numbered  point  in 
AN,  to  intersect  the  correspondingly  numbered 
line  drawn  from  center  A  to  the  circle  p'N}', 
giving  A,£>,  C,  .  .  .  N,  which  are  points  in  the  required  curve. 

Note. —  To  obtain  a  spiral  of  two  turns,  divide  AN  into  twice  as  many  parts  as 
the  circle  p'Nj'. 

Problem  68. —  To  draw  the  involute  of  a 
circle. 

Let  Ajffbe  the  given  circle.  Lay  off  on 
the  circle  equal  spaces  as  indicated  by  the  points 
I,  2,  .  .  .  5,  and  at  each  point  draw  a  tangent  to 
the  circle.  Lay  off  the  chord  lA,  once  on 
tangent  IB,  twice  on  2C,  three  times  on  jD, 
etc.,  giving  A,  B,  C,  .  .  .  G,  points  in  the  re- 
quired curve. 

Note. —  In  this  and   the    succeeding  problems  a  more  accurate  result  is  ob- 
tained by  using  the  true  length  of  the  circular  arc  instead  of  its  chord  (Prob.  73). 

Problem  69. —  To  draw  a  cycloid. 

Let  the  required  curve,  AA'" Av\  be  generated  by  point  A  lying  in  the  circle 
BDA,  which  rolls  on  the  straight  line  AE. 
Divide  the  semi-circumference  Aj6  into  six  or 
more  equal  parts  as  indicated  by  the  points 
A,  I, . . .  6.  Starting  at  point  A,  lay  off  the  chord 
A I  along  AE,  giving  points  /',  2' ,  .  .  .  6' .  Draw 
the  path,  CCvi,  of  the  center  of  the  rolling  circle. 
From  i',  2',  .  .  .  6'  erect  perpendiculars  to  intersect  CCvi  in  points  C',  C", .  .  .  C™. 
With  CA  as  radius,  centers  C,  C",  .  .  .  £>",  draw  arcs  tangent  to  AE  at  points 
l',  2' ,  .  .  .  6' .  To  find  points,  as  A',  A",  .  .  .  A"\  in  the  required  curve.  First 
method.  Make  the  chord  i'A'  equal  to  the  chord  Ai ;  make  chord  2' A"  equal  to 
chord  A2,  etc.  Second  method.  Intersect  arcs  A'l',  A"2r,  .  .  .  Avi  6'  by  lines 
drawn  parallel  to  AE,  and  passing  through  points  j,  2,  .  .  .  6. 


IOO 


GEOMETRICAL  CONSTRUCTION. 


Problem  70. —  To  draw  art  extetior  epicycloid. 

Let  the  required  curve,  A  A'"  A™,  be  generated  by  point  A,  lying  in  the  circle 
BCA,  which  rolls  on  the  circular  arc  DAE.  Divide  the  semi-circumference  Aj6 
into  six  or  more  equal  parts  as  indicated  by  the  points  A,  i,  ...  6.  Starting  at 
point  A,  lay  off  the  chord  Ai  along  the  arc  AE,  giving  the  points  j',  2' ,  .  .  .  6' . 
With  the  center,  K,  of  arc  AE  draw  arc  HGJy  the  path  of  the  center  of  the  rolling 
circle.  From  K  draw  straight  lines  through  /',  2' ,  .  .  .  6' ,  intersecting  HGJ  in 
points  G',  G",  .  .  .  Gvi.  With  radius  GA,  centers  G1 ',  G",  .  .  .  Gvi,  draw  arcs  tangent 
to  the  directing  circle  at  points  /',  2' ,  .  .  .  6' '.  To  find  points  A' ,  A",  .  .  .  Avi  in  the 
required  curve.  First  method.  Lay  off  on  arc  l'A'  the  chord  l'A'  equal  to  the 
chord  Ai ;  make  chord  2' A"  equal  to  chord  A2 ;  etc.  Second  method.  With 
K  as  center,  draw  arcs,  as  J 'A'"  and  jA™,  from  the  points  of  division  in  the 
rolling  circle  BCA  to  intersect,  as  at  A'"  and  A"',  each  of  its  successive  positions. 

Problem  71. — To  draw  a  Jiypocycloid. 

Let  the  required  curve,  FF'"FV\  be  generated  by  point  F,  lying  in  the  circle 
MLF,  which  rolls  on  the  circular  arc  DAE.  Divide  the  semi-circumference  Fj6 
into  six  or  more  equal  parts  as  indicated  by  the  points  /%/,...  6-  Starting  at  F,  lay 
off  the  chord  Fi  along  arc  AE,  giving  the  points  /',  2',  .  .  .  6' '.  With  K  as  center, 
draw  arc  NOP,  the  path  of  the  center  of  the  rolling  circle.  From  K  draw  straight 
lines  through  /',  2',  .  .  .  6',  intersecting  NOP  in  points  O',  O",  .  .  .  CK  With  FO 
as  radius,  centers  Or,  O",  .  .  .  O7"',  describe  arcs  tangent  to  the  directing  circle  at 
/',  2f,...6f.  To  find  points,  as  F' ,  F",  .  .  .  Fv*,  in  the  required  curve.  First 
method.  Lay  off  on  arc  i'F'  the  chord  i' F'  equal  to  the  chord  Fi ;  make  chord 


GEOMETRICAL  CONSTRUCTION. 


101 


2'F"  equal  to  chord  F2;  etc.  Second  method.  With  K  as  center,  draw  arcs,  as 
F' i  and  F"2,  from  the  points  of  division  in  the  rolling  circle  MLF  to  intersect,  as 
at  F'  and  F",  each  of  its  successive  positions. 

Problem  72. —  To    draw   an    interior 
epicycloid. 

Let  point  A,  lying  in  circle  BAC 
which  rolls  on  circle  ADE,  be  the  genera- 
trix. From  F,  the  center  of  the  directing 
circle,  draw  a  circle  HJG,  passing  through 
the  center  G  of  the  rolling  circle.  Start- 
ing at  point  A,  lay  off  on  the  directing 
circle  any  equal  distances,  as  indicated  by 
the  points  I,  2, .  .  .6.  Draw  iF,  2F,  . .  .$F, 
produced  to  intersect  the  path  of  the  center 
of  the  rolling  circle  in  points  Gf,  G", . . .  Gvi.  With  each  of  these  points  as  a  center, 
radius  A  G,  draw  arcs  tangent  to  the  directing  circle  at  /,  2,  . .  .  6.  From  the  tangent 
point  of  each  arc,  lay  off  the  chord  of  arc  A I  once  on  arc  I  A',  twice  on  arc  2 A", 
three  times  on  jA"f,  etc.,  giving  A',  A",  .  .  .  Avi,  points  in  the  required  curve. 

Problem  73. —  To   lay    off  on   a   straight   line  the 
length  of  a  given  circular  arc.       An  approximate  method. 

Let  ABC  be  the  given  arc.     Draw  AD  tangent  to 
arc  ABC.     Draw  chord  CA  produced.     Bisect  AC  at  E 
and  lay  off  AF equal  to  AE.     With  CFas  radius,  center  F,  intersect  AD  in  point 
G ;  then  AG  is  equal  to  arc  ABC,  very  nearly. 

Note. —  If  the  arc  subtends  more  than  about  60°,  it  should  be  subdivided 
before  using  this  construction,  which  becomes  more  accurate  the  smaller  the  sub- 
tended angle.  Thus,  if  the  arc  subtends  60°,  the  length  obtained  is  about  one  part 
in  900  too  short ;  if  30°,  about  one  part  in  15,000. 


Problem  74. —  To  lay  off  on  a  circular  arc  of  given 
radius  the  length  of  a  given  straight  line.  An  approxi- 
mate method.  ^ 

Let  AB  be  the  given  straight  line.  With  the 
given  radius,  draw  arc  ACD  tangent  to  AB.  Make  AE  equal  to  \  AB. 


With 


radius  BE,  center  E,  intersect  arc  ACD  in  point  F;   then  arc  ACF  is  equal  to 
AB,  very  nearly. 

Note. —  The  result  is  more  accurate  the  smaller  the  angle  subtended  by  the 
arc,  substantially  as  in  Prob.  73. 


CHAPTER   VI. 


SELECTION  AND  ARRANGEMENT. 

48.  The  Layout.  This  is  a  freehand  or  instrumental  sketch  in  which  is 
planned  the  general  scheme  of  a  proposed  drawing.  The  principal  requirements  in 
making  a  layout  are  taste  and  good  judgment  in  the  selection  and  arrangement  of 
the  matter  to  appear  in  the  drawing. 

While  in  office  practice  selection  and  arrangement  are  likely  to  be  restricted, 
more  or  less,  on  account  of  the  fixed  character  of  such  work,  yet,  when  opportunity 
offers,  especially  in  architectural  practice,  taste  and  good  judgment  may  be  of 
decided  value.*  As  these  are  personal  qualities,  it  is  evident  that  no  hard-and-fast 
rules  can  be  given  for  the  guidance  of  the  beginner ;  he  must  depend  largely  upon 
observation,  criticism,  and  experience. 

In  order  to  emphasize  the  difference  between  good  and  bad  selection  and 
arrangement,  first  take  a  case  illustrating  the  latter,  as  follows  :  Let  it  be  required 

to  select  eight  or  ten  geometri- 
cal constructions  from  the  pre- 
ceding chapter,  and  to  arrange 
them  on  a  sheet  of  some  given 
size. 

It  is  evident  that  the  selec- 
tion shown  in  Fig.  77  is  bad, 
because  the  problems  are  not  all 
of  the  same  general  character, 
the  last  two  problems  being 
wholly  out  of  keeping  with  the 
remaining  simple  ones.  As  to 
Fig.  77-  the  arrangement,  the  term  does 

not  apply  to  such  haphazard  placing  —  there  is  no  semblance  here  of  either  order 
or  taste. 

*  Sooner  or  later,  from  one  source  or  another,  the  student  is  sure  to  hear  it  said  that  matters  of 
taste  have  no  place  in  engineering ;  that  time  spent,  for  example,  in  making  well-formed  letters,  or  an 
effective  title,  or  in  attempting  to  make  a  design  agreeable  to  the  eye,  as  well  as  structurally  correct,  is 
time  wasted.  From  a  strictly  commercial  and  utilitarian  standpoint  this  may  be  true ;  but,  on  the  other  hand, 
some  engineers  recognize  the  fact  that  beauty  in  engineering  works,  even  in  machinery,  is  possible,  and 
that,  with  a  growing  public  appreciation,  the  element  of  beauty  will  not  only  be  demanded,  but  paid  for. 
Already  in  the  building  of  several  important  bridges  the  question  of  beauty  has  been  recognized  by  the 
engineer  and  architect  working  in  conjunction.  Apart  from  practical  considerations,  however,  a  student 
cannot  afford,  as  a  matter  of  education,  to  remain  blind  to  the  difference  between  good  and  bad  taste, 

(102) 


SELECTION  AND  ARRANGEMENT. 


103 


APPLIED    GEOMETRY 


Fig.  78. 


As  the  question  of  selection  is  inseparable  from  the  requirements  of  each  par- 
ticular drawing,  no  definite  rules  can  be  given  other  than  the  one  general  rule  that 
the  selection  should  be  consistent  with  the  purpose  of  a  drawing.  In  the  subject 
of  arrangement,  the  following  methods  are  important. 

(a)  In  designing  an  arrangement,  quicker  and  better  results  will  be  obtained  if, 
instead  of  clinging  to  mechanical  methods,  the  broader  methods  of  freehand  draw- 
ing be  adopted.  Use  a  rather 
soft  pencil,  and  start  with  the 
intention  of  spoiling  several 
sheets  of  paper,  if  necessary,  to 
secure  a  satisfactory  result — 
a  good  result  is  always  worth 
more  than  the  paper.  When 
sketching  in  the  views,  let  the 
pencil  swing  freely  over  the 
surface  of  the  paper,  in  all  di- 
rections, as  suggested  by  the 
arrows,  Fig.  78.  Let  the  mo- 
tion be  from  the  arm  rather 
than  from  the  wrist  or  fingers ; 
the  freedom  of  motion  thus  obtained  tends,  in  itself,  to  prevent  one  from  see- 
ing things  in  a  detailed,  constrained  way.  Do  not  begin  by  placing  a  problem 
up  in  one  corner  of  the  sheet,  then  another  beside  it,  then  a  third  one  close  to  the 
second,  and  so  on  until  the  sheet  is  filled ;  but  strike  out  boldly,  and  with  the  ob- 
ject of  indicating  roughly  the  shapes  and  quantity  of  the  more  important  figures, 
in  order  to  gain  quickly  a  first  impression  of  the  (tentative)  arrangement  as 
a  whole. 

In  working  for  an  arrangement,  it  is  necessary  to  take  into  account  not  only 
the  shape  and  quantity  of  the  problems,  but  also  the  shape  and  quantity  of  the 
spaces  between  problems,  and  between  problems  and  the  border  line  of  the  sheet. 
First  place  the  dominant  or  most  important  problem,  as  A,  Fig.  78,  thereby 
breaking  up  the  regular  (rectangular)  figure  of  the  sheet  into  an  irregular  shape. 
Next  place  an  important  problem,  as  B  and  C,  in  a  manner  best  calculated  to  fill 
the  irregular  space  satisfactorily,  thereby  breaking  up  the  surface  into  new  irreg- 
ular spaces,  the  shape  and  size  of  each  of  which  must  be  considered  in  placing  ad- 
ditional problems,  as,  for  example,  those  shown  in  Fig.  79. 

When  a  rough  basis  for  what  appears  to  be  a  satisfactory  arrangement  is  se- 
cured, as  in  Fig.  79,  then  work  out  the  problems  with  more  care  freehand,  or  with 
ruler  and  compass,  but  only  to  the  extent  necessary  to  serve  as  a  basis  for  the  fin- 


104 


SELECTION  AND  ARRANGEMENT. 


APPUE.O     GEOMETRY 


Fig-  79- 


ished  sheet.  In  rearrangements  it  is  convenient  to  make  changes  on  tracing  paper 
placed  over  the  first  layout,  and  for  succeeding  changes  to  use  a  fresh  sheet  of  trac- 
ing paper  placed  over  the  pre- 
ceding one.  In  some  cases  it  is 
convenient  to  cut  up  the  sheet 
so  that  the  problems  —  or  views 
of  an  object  —  may  be  moved 
about  until  the  desired  arrange- 
ment is  obtained,  after  which 
the  loose  pieces  may  be  pasted 
in  position. 

(^)  Forms  of  arrangement. 
A  layout  should  be  begun  with 
some  definite  scheme  or  form  of 
arrangement  in  mind.  If  it  is 
found  that  the  subject  matter 
does  not  lend  itself  to  a  proposed  scheme,  other  forms  may  be  experimented  with 
until  a  form  is  obtained  which  proves  satisfactory. 

Symmetrical  lateral  arrangements  ;  balance.  If  the  problems  —  or  views  —  on 
a  sheet  be  regarded  as  so  many  actual  zveights,  then,  in  viewing  the  sheet,  it  may  be 
considered  whether  the  weights  on  opposite  sides  of  the  center  lines  of  the  sheet 
counterbalance.  In  an  arrangement  symmetrical  with  respect  to  the  vertical  center 
line  of  a  sheet,  an  appearance  of  stability  may  be  obtained  by  making  the  problems 
placed  on  the  center  line  larger  than  those  placed  on  either  side. 

Symmetry  with  respect  to  a  central  draiving.  The  central  drawing  should  be 
the  largest  on  the  sheet,  and  the  other  drawings  should  balance,  both  laterally  and 
vertically,  with  respect  to  the  central  drawing. 

Abstract  arrangement.  In  this  form  the  problems  may  be  placed  irregularly, 
but  exaggerated  and  grotesque  effects  should  be  avoided.  An  effect  of  stability 
may  be  secured  by  making  the  weights  of  the  problems  placed  low  on  the  sheet 
somewhat  heavier  than  of  those  placed  high  on  the  sheet  —  or  by  giving  the  ar- 
rangement, as  a  whole,  the  form  of  a  truncated  pyramid  with  slightly  sloping  sides. 
The  problems  should  fill  the  sheet ;  that  is,  an  arrangement  should  appear 
neither  crowded  nor  scant. 

In  Figs.  80,  8 1,  82,  83,  and  84  are  given — as  examples  and  for  criticism  — 
specimens  of  students'  work  in  selection  and  arrangement,  reproduced  from  draw- 
ings 1 8"  x  26".     Criticisms :  — 

Fig.  80.     The  sheet  is  sparsely  filled.     The  left-hand  two  problems  of  the  lower 
line  are  too  small ;  the  title  is  too  large  compared  with  the  size  of  the  problems. 
Fig.  81.     The  sheet  is  crowded. 


EXAMPLES  OF  SELECTION  AND  ARRANGEMENT. 


Avoid 


105 


APPLIED  GEOMETRY 


Avoid 


Fig.  80. 


APPLIED   GEOMETRY 


Fig.  8 1 


io6 


EXAMPLES  OF  SELECTION  AND  ARRANGEMENT. 


APPLIED 
GEOMETRY 


Fig.  82. 


APPLIED 
GEOMETRY 


, , J ,,— -. 

k-i    •  r  ... — 


Fig.  83. 


SELECTION  AND  ARRANGEMENT  —  STUDY  PLATE  6. 


107 


Fig.  82.  The  arrangement  is  slightly  top-heavy,  the  two  problems  at  the  top 
of  the  sheet  being  too  large.  If  these  problems  were  smaller,  the  remaining  six 
problems  would  appear  too  low  on  the  sheet. 

Fig.  83.  The  side  problems  of  the  middle  horizontal  line  are  rather  small  for 
the  central  problem ;  the  two  problems  on  the  top  line  are  somewhat  large ;  and 
the  spacing  of  the  side  lines  of  problems  is  a  trifle  close  compared  with  the  spacing 
of  the  problems  in  the  horizontal  lines. 


APPLIED 
GEOMETRY 


Fig.  84. 

Fig.  84.  The  lower  left-hand  problem  appears  farther  from  the  bottom  border 
line  than  does  the  lower  right-hand  problem.  This  is  due  to  not  allowing  for  the 
emptiness  of  the  lower  portion  of  the  larger  circle  ;  it  is  the  group  of  construction 
lines  which  here  attracts  the  eye. 

STUDY  PLATE   6. 

For  selection,  arrangement,  and  precise  rendering. 

It  is  required  to  make  a  finished  drawing,  which  shall  contain  problems  selected 
from  Problems  I  to  18,  Chapter  V.,  and  also  include  one  of  the  following  titles,  to 
be  designed  by  the  student :  "  Geometrical  Construction"  ;  "  Selection  and  Arrange- 
ment ";  "Applied  Geometry."  Use  Whatman's  hot-pressed  paper;  the  sheet  is 


io8  STUDY  PLATES  6,  7,  AND  8. 

to  be  10"  x  14",  with  a  ruled  border  line  8"  x  12".  Make  the  layout  on  any  spare 
paper,  and  do  not  begin  the  finished  drawing  until  the  arrangement  has  been  fully 
decided. 

PENCILING.  The  final  sheet  should  be  drawn  very  accurately  ;  make  the  lines 
full. 

INKING.  Ink  according  to  either  a  or  b,  Art.  47,  and  make  the  width  of  line 
the  same  as  that  of  the  lines  A,  B,  and  C,  Fig.  55.  Letter  the  title;  also  "Plate 
6,"  your  name,  and  the  date.  The  letters  must  be  drawn  (Art.  41). 

STUDY  PLATE  7. 

For  selection,  arrangement,  and  precise  rendering. 

It  is  required  to  make  a  finished  drawing,  which  shall  contain  problems  selected 
from  Problems  19  to  40,  Chapter  V.,  and  a  title.  Use  Whatman's  hot-pressed  paper; 
the  sheet  is  to  be  14"  x  20",  with  a  ruled  border  line  12"  x  18".  Proceed  accord- 
ing to  the  directions  for  Study  Plate  6. 

STUDY  PLATE  8. 

For  selection,  arrangement,  and  precise  rendering. 

It  is  required  to  make  a  finished  drawing,  which  shall  contain  problems  selected 
from  Problems  41  to  74,  Chapter  V.,  and  a  title.  The  drawing  is  to  be  20"  x  26", 
with  a  ruled  border  line  18"  x  24".  Use  Whatman's  hot-pressed  paper.  Proceed 
according  to  the  directions  for  Study  Plate  6. 


CHAPTER   VII. 


OBJECT   DRAWING. 

49.  In   engineering,  architectural,  and  shop  construction,  objects  are  com- 
monly  represented   by    means   of  geometrical   views  called  projections.     For  the 
complete  representation  of  any  object  two  or  more  projections  are  necessary,  each 
being  a  different  view  of  the  object.     In  order  to  comprehend  or  read  a.  projection 
drawing,  it  is  necessary  to  combine  the  several  views  in  imagination,  thereby  form- 
ing a  mental  picture  of  the  object   as  a  whole.     The  ability  to  read  projections 
easily,  usually  requires  extended  practice,  which  is  best  obtained  through  the  study 
of  descriptive  geometry  and  a  considerable  amount  of  drawing  from  objects. 

50.  Sketching  and  Measuring,     (a)     The  sketches.     As,  in  practice,  objects 
from  which   drawings  are  to  be  made  are  usually  not  near 

by,  it  is  necessary  to  make  the  final  drawings  from 
sketches  showing  the  character  and  measurements  of  the 
object.  The  same  procedure  should  be  adopted  when 
drawing  from  class-room  models ;  that  is,  the  model  should 
be  sketched  and  measured,  and  then  put  aside,  so  that  the 
subsequent  work  shall  be  wholly  from  the  sketches. 

(b)  Character  of  the  sketch  rendering.     The  sketches 
must  not  be  loosely  rendered,  as  when  experimenting  for 
an  arrangement  (a,  Art.  48),  but  must  be  rendered  in  single 
line,   carefully   and   directly  —  thus    giving   the    sketch  a 
somewhat  set  appearance  —  and  with  little  or  no  erasure, 
or  preliminary  suggestion.     The  lines  should  be  firm,  crisp, 
and  accurately  placed  with  respect  to  the  vertical  and  the 
horizontal. 

(c)  The   measurements.      Take   the    measurements 
with  the  two-foot  rule  and  the  calipers  (see  materials,  p.  2). 
Care  should  be  taken  to  make  well-formed  and  legible  numer- 
als, signs,  and  arrow  heads.     The  dimensions,  other  data, 
and  remarks  may   be  stroke  rendered  or  neatly  written. 
Center,  extension,  and  dimension  lines  may  be  ruled. 

All  sketches  made  in  connection  with  the  exercises  in  object  drawing  should 
be  placed  in  the  note  book  (see  materials,  p.  2),  and  this  book  should  be  used  for 
no  other  purpose. 

(109) 


I  IO 


OBJECT  DRAWING  —  SKETCHING  AND  MEASURING. 


(d}  As  a  first  example  of  sketching  and  measuring,  take  the  sketch,  Fig.  86, 
made  from  a  wooden  model  of  a  locomotive  hand-rail  stud.  The  stud,  A  (Fig.  85), 

through  which  passes  the  hand  rail  B,  rests  on 
the  horizontal  portion,  C\  of  a  bracket  riveted 
«  ITM  /•  ^ — -v  \      to  the  boiler.     The  necessary  sketches  of  this 

/I  *tL  P]  It          \\ 

u  oj>  W I          If          \\     object  include :  a  front  view  or  front  elevation 

V^.*—-    2$'D-£&\  |       \V_X/      (A,    Fig.    86);    a  side  view  or  side  elevation 

(B),  as  seen  in  the  direction  of  the  arrow  X, 
Fig.  85  ;  and  a  lower  end  or  bottom  view  (in- 
verted plan},  C,  as  seen  in  the  direction  of 
the  arrow  Y,  Fig.  85.  The  necessary  meas- 
urements of  the  hand-rail  stud  are  given  in 
Fig.  86. 

(e)  Sketches  of  another  drawing  room 
model,  Fig.  87,  are  given  in  Fig.  88.  The  ob- 
ject is  a  cabinet  maker's  clamp  (see  also  Plates 
13  and  14).  The  parts  of  the  clamp,  A  and 
B  (Fig.  87),  which  compress  the  glued  pieces, 
C,  C,  C,  C,  are  attached  to  a  wooden  bar,  F. 
The  block,  A,  is  attached  to  the  bar  by  the 
binder,  G.  The  head  of  the  clamp,  B,  is  at- 
tached to  the  bar  by  the  iron  strap,  H,  which 
bears  against  the  plate,  J.  In  order  that  the 
sketches  might  be  of  a  size  adapted  to  the  page 
of  the  sketch  book,  parts  of  the  object  were 
broken  and  brought  together  as  shown  (Fig. 
88).  The  order  in  which  the  sketches  were  made  is  as  follows :  B  (projection 
in  the  direction  Zt  Fig.  87),  B'  (projection  in  the  direction  Y,  Fig.  87),  B"  (pro- 
jection in  the  direction  X}\  A,  A',  D,  D',  etc.  It  should  be  noted  that  the 
same  letter  is  used  in  Figs.  87  and  88  to  indicate  corresponding  parts  of  the 
clamp. 

51.  Selection  and  Arrangement ;  the  Layout.  To  illustrate  further  methods 
in  object  drawing,  let  it  be  supposed  that  it  is  required  to  make  a  finished  trac- 
ing on  cloth  of  a  mechanical  drawing  to  be  made  from  the  sketches  of  the 
hand-rail  stud,  Fig.  86,  and  also  that  the  tracing  shall  be  a  satisfactory  example  of 
symmetrical  arrangement.*  The  size  of  the  tracing  is  to  be  14"  x  20",  with  a  ruled 
border  line  I3"x  19"  (i"  margin).  The  first  step  is  to  decide  upon  an  arrangement. 

*  A  symmetrical  arrangement  is  chosen  merely  as  an  example  ;  more  often  an  abstract  arrangement 
(b,  Art.  48)  appears  to  be  necessary  (see  Plates  13,  14,  and  15). 


Fig.  86. 


OBJECT   DRAWING — THE  LAYOUT. 


in 


For  this  purpose  any  spare  paper  is  suitable ;  a  border  line  of  the  required  size 
should  be  ruled,  a  soft  pencil  used,  and  the  procedure  should  be  in  accordance  with 
a,  Art.  48. 


NOTE. —  On  account  of  the  small  size  of  this  cut,  some  of  the 
dimensions  are  omitted. 


Fig.  88. 

A  glance  at  the  overall  measurements,  Fig.  86,  will  show  that,  if  the  projec- 
tions of  the  stud  are  not  to  appear  lost  on  the  sheet,  the  drawing  cannot  be  made 
to  a  reduced  scale,  but  must  be  full  size.  It  will  also  be  seen  that  the  number  of 


ii2     OBJECT  DRAWING  —  THE  LAYOUT  —  COLLECTIVE  RENDERING. 


views,  Fig.  86,  necessary  to  represent  the  stud  are  not  sufficient  to  fill  the  sheet. 
But  in  view  of  the  requirement  that,  besides  representing  the  stud,  the  drawing 
shall  be  a  satisfactory  example  of  arrangement,  the  number  of  projections  need  not 
be  restricted,  as  in  the  case  of  a  working  drawing  (b,  Art.  64),  to  those  projections 
which  are  actually  necessary ;  hence  a  section  may  be  added  and  a  title  introduced. 
A  first  arrangement  is  illustrated  in  Fig.  89.  In  this  sketch  the  views  fill  the  sheet 


Fig.  89.  Fig.  90. 

satisfactorily,  but  the  elevation  at  the  right-hand  side  of  the  sheet  does  not  balance 
the  section  at  the  left-hand  side ;  the  title  hardly  balances  the  lower  left-hand 
section,  and  the  lower  views  are  crowded.  A  second  scheme  of  arrangement  is 
shown  in  Fig.  90.  Here  the  projections  on  either  side  of  the  central  figure  bal- 
ance each  other,  but  the  eye  is  attracted  to  the  right-hand  side  of  the  sheet  on 
account  of  the  heavier  effect  due  to  the  cross  hatching.  The  title  and  the  views 
on  either  side  of  the  title  are  crowded ;  if  the  size  of  the  title  is  reduced  to  give 
a  satisfactory  spacing,  it  will  appear  too  small.  The  third  scheme,  Fig.  91,  the^ 
one  finally  adopted  (see  Plate  12),  appears  to  be  the  best  of  the  examples  given. 
The  stronger  black-and-white  value,  due  to  the  cross  hatching,  is  kept  central ;  and 
the  space  in  the  lower  right-hand  corner  is  filled  by  the  additional  section. 

52.  The  Drawing  for  Tracing ;  Collective  Rendering.  (Methods  continued.) 
The  locations  of  the  views  in  the  pencil  drawing  for  the  tracing  are  taken  from  the 
layout.  Of  special  importance  is  the  treatment  of  the  projections,  which  should 


OBJECT  DRAWING  —  COPYING  —  SCREW  THREADS. 


be  drawn  in  combination ;  that  is,  in  penciling,  no  one  projection  should  ever  be 
carried  to  completion,  then  another  completed,  then  another,  and  so  on,  but  at  each 
stage  of  the  drawing  each  projection  should  shoiv  that  it  lias  received  equal  attention. 

Tlie  projections  of  an  object  should  always 
be  laid  out  with  reference  to  their  center  lines. 
(See  b,  Study  Plate  9.) 

53.  Copying  as  a  Preliminary  to  Object 
Drawing.     A   great  deal  can  be  learned  by 
copying    good    examples    of    drawing,    from 
the   originals,    or  from  prints  of   the   same. 
Mere  automatic  imitation,  however,  of  a  draw- 
ing or  print,  unaccompanied   by  thought   of 
the  meaning  and  application  of  the  construc- 
tion and  technique   there  represented,  is  of 
little  value  ;  but  if  the  copying  serves  to  im- 
press correct  methods  of  rendering,  to  culti- 
vate taste  and  good  judgment,  and  to  afford 
practice  in  reading  drawings,  then  there  is  no 
question  that  a  reasonable  amount   of   time 
given   to    copying   is   well    spent.     Students 
appear   to  be   particularly   weak   in    making 
neat  and  rapid  sketches,  in  rendering  dimen- 
sions on  sketches,  and  in  sketching  layouts. 

When  this  is  the  case,  the  student  should  not  expect  to  correct  his  deficiency 
through  the  sketching  connected  with  a  required  amount  of  object  draw- 
ing, as  the  time  here  spent  in  sketching  is  relatively  small  compared  with  the 
time  necessary  for  making  the  mechanical  drawings.  He  should  give  special 
attention  to  sketching,  and  to  sketch  dimensioning  as  such,  making  it  a  practice 
to  sketch  any  object  at  hand  at  every  opportunity,  though  it  be  for  only  five 
minutes  at  a  time.  In  this  connection  the  preliminary  exercises  in  sketching 
indicated  in  Study  Plates  9-13  are  important. 

54.  Screw  Threads,     (a]     Single  and  double  threads  ;  pitch.     If  a  point  were 
carried  along  an  edge,  as  EFGHJ,  of  the  actual  thread  represented  in  A,  Fig.  92, 
it  would  be  seen  that,  in  passing  from  point  E  to  point  Jt  vertically  over  E,  the  thread 
makes  one  turn  about  the  axis  of  the  screw,  and  that  the  screw  has  but  one  thread. 
The  rise  or  advance,  EJ,  of  the  thread  in  making  one  turn  is  termed  its  pitch,  and, 
in  a  single  threaded  screw,  the  pitch  is  equal  to  the  combined  widths  of  the  thread 
and  the  groove  (see  EJ,  A,  Fig.  92). 

If,  in  following  a  thread,  as  at  EFGHJ,  B,  Fig.  92,  an  intervening  thread  is 


OBJECT  DRAWING — SCREW  THREADS. 


seen  between  points  E  andy,  the  screw  evidently  has  two  threads,  and  is  said  to  be 
double  threaded.  In  this  case  the  pitch,  EJ,  is  equal  to  the  combined  widths  of  the 
A  B  two  threads  and  the  two  grooves. 

If  the  front  of  a  thread  ascends  from 
left  to  right,  as  from  E  toy  in  Fig.  92,  the 
screw  is  said  to  be  right-handed ;  if  the  front 
of  the  thread  ascends  from  right  to  left,  the 
screw  is  left-handed. 

(b)  The  shape  and  size  of  a  screw 
thread.  The  actual  shape  and  size  of  a 
thread  are  determined  by  the  shape  and  size 
of  its  cross  section  (Fig.  93)  taken  in  a 
plane  passing  through  the  axis  of  the  screw. 
The  size  of  a  thread,  while  determined  by 
the  size  of  its  section,  is  commonly  expressed 
by  stating  the  number  of  sections  in  one  inch, 
measured  parallel  to  the  axis  of  the  screw, 
thus :  i  o  threads  to  an  inch  (usually  given 
in  the  form  IO  Th.  or  IO  Thds.}. 

(c\     Measuring  a  screw.    When  familiar 


92- 


V-THREAD          WHITWORTH 


with  the  various  thread  sections,  Fig.  93,  the  shape  of  a  particular  thread  can  be 
easily  identified  from  inspection.  There  should  be  recorded  in  the  sketch  :  the 
shape  of  the  thread ;  the  number  of  threads  to  an  inch  ;  and  whether  the  thread 
is  single  or  double.  The  necessary  measurements  of  a 
threaded  bolt  are  as  follows :  total  length,  including  the 
head ;  length  of  body,  including  threaded  portion  ;  length  of 
the  threaded  portion ;  diameter  of  body ;  height  and  short 
diameter  of  the  head. 

(d)  Drawing  a  screw  thread.  The  drawing  must  be 
begun  by  making  a  longitudinal  section  A,  Fig.  94,  taken 
through  the  axis  of  the  screw.  For  a  complete  representa- 
tion, it  is  necessary  to  show  the  curvature  of  the  thread  (see 
helix,  descriptive  geometry) ;  but  ordinarily,  in  object  drawing, 
straight  lines,  as  FH,  HM,  JK,  and  KL,  B,  Fig.  94,  are  sub- 
stituted for  the  curves. 

In  each  of  Figs.  94-97  are  illustrated  four  things, 
namely :  at  A,  the  pencil  construction ;  B,  the  directions  of 


I 
SQUARE 


U.S.  STANDARD 


SECTIONS    OF 
SCREW   THREADS 


Fig-  93- 


the  front  and  back  edges  of  the  thread ;  C,  the  front  of  the  completed  thread ; 
and  D,  the  completed  thread  as  seen  in  a  section  of  a  tapped  hole  or  nut. 


OBJECT  DRAWING  —  SCREW  THREADS. 


(e)  Construction  of  a  single,  right-hand,  V  thread,  4  threads  to  an  inch.  (Fig. 
94.)  Lay  off  EG  equal  to  the  given  diameter  of  the  screw,  and  draw  the  contour 
elements,  JSFand  GH — the  entire  length  of  the  threaded  portion.  Set  the  scale  to 
the  element  EF,  and,  starting  at  point  E,  lay  off  \"  distances,  as  1-2,  2-3,  the 
entire  length  of  the  threaded  portion.  With  the  30°  triangle,  draw  the  section, 
iR2,  of  the  groove,  and  through  point  R  draw  the  line  RS  parallel  to  EF.  Com- 
plete the  sections  of  the  groove  and  thread  along  the  left-hand  side  of  the  screw, 
and,  as  a  check,  see  that  the  roots,  as  R  and  S,  of  the  thread  fall  accurately  in  the 
line  RS.  From  point  R,  draw  RP  perpendicular  to  line  EF,  intersecting  element 


Fig.  94- 


Fig-  95- 


Fig.  96 


Fig.  97. 


GH  in  point  P,  thus  locating  —  since  the  thread  is  single  —  a  point  of  the 
thread.  Starting  at  point  P,  draw  one  triangle  representing  a  section  of  the 
thread,  and  also  the  line  TU  containing  the  roots  of  the  thread.  Lay  off  from  the 
scale  the  positions  of  the  points  of  the  threads,  and  complete  the  sections  at  the 
right-hand  side  of  the  screw.  Having  thus  drawn  the  sections  of  the  thread, 
note  (at  /?),  the  one  turn  FHM,  zndJKL,  of  the  point  and  root  edges  respectively ; 
then  draw  the  visible  edges  of  the  screw,  and  of  the  nut,  as  shown  at  C  and  D. 
The  end  of  the  screw  in  the  drawing  is  usually  finished  by  an  arc  of  a  circle,  as  X, 
Fig.  94,  described  from  any  appropriate  point,  as  O,  lying  in  the  axis  of  the  screw. 

(/)  Construction  of  a  double •,  left-hand,  V  thread,  2  threads  to  an  inch. 
(Fig.  95.)  Observe  that  the  pitch  is  i  inch,  and  that,  since  the  thread  is  double, 
the  points  of  the  sections  on  opposite  sides  of  the  screw  fall  opposite  each  other  ; 
otherwise  the  construction  is  the  same  as  in  Fig.  94. 

(g)  Construction  of  a  U.S.  standard  thread,  4  threads  to  an  inch.  (Fig. 
96.)  Draw  the  contour  elements,  Z  TV  and  OV,  of  the  screw.  Outside  of  LN ',  and 
O  V,  at  a  distance  equal  to  |  of  the  pitch  of  the  screw,  draw  EF  and  PH.  Using 


n6 


OBJECT  DRAWING  —  CONVENTIONAL  SCREW  THREADS. 


EFand  Pffas  corresponding  to  EFand  PH  in  Fig.  94,  construct  the  sections  of 
a  V  thread  of  the  given  pitch  (see  e).  Outside  of  RS,  and  777,  at  a  distance  equal 
to  |  the  pitch  of  the  screw,  draw  L' N'  and  O'  V .  Connect  the  points  of  the  sec- 
tions as  shown  at  C  and  1),  Fig.  96. 

(//)  Construction  of  a  single,  square  thread,  4  threads  to  an  inch.  The  con- 
struction is  evident  from  Fig.  97. 

55.  Conventional  Screw  Threads.  Any  of  the  conventions  shown  in  Figs.  98 
and  99  may  be  used  according  to  preference  or  requirement.  The  constructions  are 
as  follows  :  — 

(a)  Convention  A,  Fig.  98.  Starting  at  point  D,  lay  off,  for  the  entire  length 
of  the  left-hand  contour  element,  any  assumed  distance,  as  DF ;  at  E,  opposite  D, 


Fig.  98. 


Fig.  99. 


lay  off  the  same  distance,  EG,  on  the  right-hand  contour  element.  Connect  the 
points  F  and  E ;  then,  by  sliding  the  triangle,  draw  lines  parallel  to  FE,  passing 
through  the  points  laid  off  on  the  left-hand  element. 

The  distance  laid  off  on  the  elements  need  not  be  the  actual  pitch  of  the 
thread,  but  any  convenient  distance  which  gives  a  satisfactory  spacing  for  the 
parallel  lines. 

(&)  Convention  B,  Fig.  98.  First  draw  the  thread  in  pencil  according  to  A, 
Fig.  98.  Make  the  distances  JK  and  LM  each  equal  to  the  unit,  as  /A7,  of  the* 
vertical  spacing,  and  draw  KK'  and  LL' .  When  inking  the  convention,  begin -and 
end  the  lines  representing  the  thread,  alternately,  at  the  lines  KK'  and  LL' .  Thus, 
for  example,  draw  from  point  N  to  line  LL' ,  and  from  point  P' ,  in  KK' ,  to  line 
MQ  (see  the  lower  portion  of  the  figure). 

(c]  Convention  C,  Fig.  98.  First  draw  the  thread  according  to  the  pencil 
construction  in  B,  Fig.  98.  Ink  the  convention  as  shown  in  the  figure.  The 


OBJECT  DRAWING — CHAMFER  OF  NUTS  AND  BOLT  HEADS.      117 


wide  lines  should  be  first  represented  by  two  narrow  lines,  and  afterward  filled  in 
as  described  for  the  wider  lines  in  section  lining  (b,  Art.  38). 

(d]  Convention  A,  Fig.  99.     The  pencil  construction  is  the  same  as  for  con- 
vention B,  Fig.  98.     Make  DE  and  FG  each  equal  to  |  of  CE,  and  draw  lines 
DH  and  GJ.     Ink  the  convention  as  shown  in  the  figure. 

(e)  Convention  B,  Fig.  99.     The  thread  should  be  drawn  according  to  e,  Art. 
54.     The  black  areas  represent  conventional  shadows,  the  curved  edges  of  which 
may  be  located  as  follows  :  Lay  off  distance  KL  equal  to  |  of  KN,  and  draw  line 
LU.     Make  MN  equal  to  \  of  LN,  and  draw  MV.     Through  the  points,  as  P 
and  Q,  in  which  L  U  and  MV  intersect  the  root  of  a  thread,  draw  a  circular  arc, 
center  found  by  trial,  tangent  to  the  point  of  the  thread,  as  at  O,     Through  the 
center,  R,  of  .this  arc,  draw  line  OT.     With  the  same  radius,  and  keeping  the 
center  always  in  line  OT,  draw  the  arcs  for  all  the  shadows,  as  indicated  by  the 
arrows.     Fill  in  the  shadows  with  India  ink  applied  with  a  brush  or  a  writing  pen. 

56.  Chamfer  of  Nuts  and  Bolt  Heads.  Let  Fig.  TOO  represent  the  head  of  a 
bolt  supposed  to  revolve  about  its  axis  ad,  while  the 
tool,  Z,  cuts  off  or  chamfers  the  edges,  JQ,  QX,  XR, 
etc.  The  surface  BFNUWTP,  etc.,  of  the  chamfer 
is  a  portion  of  the  surface  of  the  imaginary  cone, 
def  :  the  right-hand  edge,  FNU,  of  the  chamfer  is  a 
circle,  since  it  is  the  boundary  of  a  right  section  of 
the  cone  def  ;  and  the  left-hand  boundary  BEHMW, 
etc.,  is  a  series  of  six  equal  hyperbolic  arcs,  being  the 
intersection  of  the  cone  def,  by  the  six  faces  of  the 
bolt  head.  Since  the  base  of  the  head  is  perpendicular 
to  the  axis,  ab,  the  edges  AB,  GH,  OP,  and  VW  are 
cut  off  the  same  length  ;  likewise  the  distances  DE, 
LM,  and  ST  are  equal.  In  practical  drawing,  the 
hyperbolic  curves  are  always  represented  by  arcs  of 
circles;  the  position  of  the  arcs  may  be  determined 
as  follows  :  — 


Fig.  100. 


(a)  Construction.  Through  the  lowest  point,  A,  Fig.  101,  in  the  chamfer 
(located  by  measuring  the  edge  AB),  draw  the  line  AD  making,  in  this  case,  45° 
with  the  top  surface  of  the  bolt  head.  With  radius  CD,  draw  the  circle  D'G',  rep- 
resenting the  top  edge  of  the  chamfer.  The  lowest  points  in  the  chamfer,  as  E,  A, 
and  E",  lie  in  the  vertical  edges  of  the  head.  The  highest  points  in  the  chamfer,  as 
H,  N,  and  N",  lie  in  the  center  lines  of  the  vertical  faces.  Pass  the  plane  C  K'f  , 
containing  the  axis  of  the  head  and  bisecting  its  front  face  ;  this  plane,  revolved, 
corresponds  to  the  half  side  view  C"K"  J".  Layoff  C"G"  equal  to  C'  G'  ,  and 


u8       OBJECT  DRAWING — CHAMFER  OF  NUTS  AND  BOLT  HEADS. 

through  point  G"  draw  the  line  G"H",  at  45°,  thus  determining  point  H",  which  is 
the  highest  point  of  the  chamfer,  lying  in  the  center  line  HJ  of  the  front  face  of 


YI  VIP  I       ir.y/'  '  *     |c"  ii 

-  -'- A-  -    lj?,I  Z^Sl 


Fig.  101. 


102. 


the  head.     Project  the  highest  and  lowest  points  in  the  curves  as  shown.     Find 

each  center,  as  P,  from  which  to  describe  the  circular  arcs,  according  to  b,  Art.  45. 

A  30°  conical  chamfer  on  a  square  head  is  shown  in  Fig.   102.     A  spherical 

chamfer  is  shown  in  Fig.  103.     It  will  be  seen  that  the  chamfer  is  made  only  deep 


t 


Fig.  103. 

enough  to  complete  the  curve  on  each  face  of  the  nut ;  the  lower  edges  of  the 
chamfer  are  therefore  tangent  to  its  upper  edge. 

57.  Doubtful  Lines.  In  object  drawing  it  frequently  happens  that,  on  account 
of  rounded  corners  or  other  curved  surfaces,  a  part  of  an  object  shows  no  definite' 
line  boundary ;  hence,  theoretically,  the  part  cannot  be  expressed  by  an  outline. 
When,  in  such  cases,  the  question  arises  whether  a  line  should  be  put  in  or  omitted, 
it  is  best  to  ignore  geometrical  truth,  if  the  drawing  will  be  made  clearer  thereby. 
Examples  :  — 

(a)     Detail  of  the  clamp,  A,  B,  and  C,  Fig.  104.     (See  also  Plate  7J.)     The 
strictly  correct  projection,  B,  can  show  no  interior  lines,  since  all  corners  of  the 


OBJECT  DRAWING  —  DOUBTFUL  LINES  —  SHADE  LINES.          119 

object  are  slightly  rounded,  as  shown  in  the  boundaries  of  A  and  B.     The  more 
satisfactory  drawing,  C,  is  obtained  by  putting  in  the  doubtful  lines. 

(b}      The  angle  iron,  D,  £,  F,  Fig.  104.     The  projection  D  is  correct ;  but  the 
addition  of  the  doubtful  lines  in  the  projection  E  makes  this  view  the  clearer. 


~~LT 


Fig.   104. 


(c)  The  ornamental  terminations  of  a  hand-rail  stud,  G,  H,J,  K,  Fig.  104, 
(See  also  Plate  12.)  In  the  form  G,  it  is  clear  that  there  should  be  no  line  drawn 
from  L  to  M ' ;  in  the  form  Jt  it  is  equally  clear  that  there  should  be  a  line  from  P 
to  Q.  Forms  //and  K  are  the  same  ;  the  former,  without  a  line  drawn  from  JVto 
O,  is  correct ;  but  the  latter,  showing  the  doubtful  line,  RS,  seems  preferable. 

58.  Shade  Lines.  If  rays  of  light  from  any  source  be  supposed  to  fall  on  an 
object,  some  of  its  faces  will  be  in  the  light,  the  rest  in  shadow.  The  edges  of  the 
object  that  separate  its  light  from  its  dark  surfaces  are  called  shade  lines.  These 
lines  are  indicated  in  a  drawing  by  their  width,  which  is  greater  than  that  of  any 
other  lines  in  the  same  drawing.  Shade  lines  may  be  used  to  make  a  drawing 
more  effective  in  appearance,  and,  to  a  limited  extent,  to  explain  form. 

(a)  Theory  of  shade  lines  ;  rectangular  objects.  Let  B,  Fig.  105,  represent 
a  cube  with  its  base  horizontal.  The  cube  is  supposed  to  be  lighted  by  parallel 
rays,  the  direction  of  which  is  represented  by  the  diagonal,  ed,  of  the  cube  (arrow 
X),  which  makes  the  angle,  /3,  of  35°  15'  52"  with  all  faces  of  the  cube.  It  will 
be  seen  that  the  faces  abfe,  efhg,  and  aegc  receive  the  light,  while  the  remaining 
faces  are  in  shadow  ;  hence  the  shade  edges  of  the  cube  are  those  forming  the 
boundary  abfhgc.  Next,  let  the  cube  be  represented  by  the  projections  A  and  C 
(elevation  and  plan).  To  determine  the  shade  lines  of  the  projections,  it  is  nec- 
essary also  to  represent  the  light  by  means  of  projections  of  its  rays.  The  eleva- 


I2O 


OBJECT  DRAWING  —  SHADE  LINES. 


tion  Xv  (B}  of  the  ray  X,  coincides  with  the  diagonal,  ad,  of  the  back  face  of  the 
cube,  and  therefore  takes  a  direction  downward  and  to  the  right  at  45°  with  the  hori- 
zontal, and  is  so  represented  in  the  elevation,  A,  of  the  cube.  The  plan,  X h  (B)  of 
the  ray  X,  coincides  with  the  diagonal,^/,  of  the  base  of  the  cube,  and  therefore  takes 
a  direction  backward  and  to  the  right  at  45°  with  the  horizontal,  and  is  so  repre- 
sented in  the  plan,  C,  of  the  cube.  Now,  by  reading  in  combination  the  elevation 
and  plan  of  both  object  and  rays,  the  shade  lines  may  be  determined.  Thus,  for 
example,  the  elevation  (A)  shows  that  the  top  surface,  abfe,  of  the  plan  (C)  is  in 
light ;  the  plan  shows  that  the  back  surface,  abdc,  is  in  shadow ;  hence  the  line  ab, 
representing  the  (shade)  edge  separating  the  two  surfaces  in  question,  is  a  shade  line. 


Fig.  105. 

A  cylinder.  Let  J,  Fig.  105,  represent  a  cylinder,  with  its  base  horizontal, 
inscribed  in  a  half  cube,  as  indicated  by  the  diagonals  ^  and  Xh.  The  upper  base, 
ad,  is  in  the  light ;  the  lower  base  is  in  shadow.  The  ray  of  light,  X,  is  tangent  to 
the  curved  lateral  surface  at  point  b  ;  therefore,  the  element  ac,  passing  through 
point  b,  separates  the  light  from  the  dark  portion  of  the  curved  surface,  and  is  a 
shade  line.  The  element  de,  diametrically  opposite  ac,  must  also  be  a  shade  line ; 
hence,  the  entire  shade-line  boundary  of  the  cylinder  is  the  broken  line  afdegca. 

As  a  preliminary  to  object  drawing,  further  consideration  of  the  theory -of 
shade  lines  is  unnecessary.  To  determine  all  shade  lines,  in  all  cases,  requires  an 
extensive  knowledge  of  the  theory  of  shades  and  shadows  —  a  subject  useful  in 
certain  architectural  drawing  and  for  the  training  it  affords,  but  of  no  practical  use 
in  construction  drawing,  since  the  process  requires  much  time,  and  in  many  cases 
the  shade  lines  become  so  complicated  that  they  are  more  likely  to  obscure  than  to 
explain  the  form  of  an  object. 


OBJECT  DRAWING  —  SHADE  LINES.  121 

In  practice  there  is  no  general  understanding  in  regard  to  shade  lines ;  the 
architect  shades  his  drawings  in  one  way,  the  engineer  in  another.  Then,  drafts- 
men differ  in  opinion  as  to  whether  particular  lines  should  be  shaded  or  not,  and 
this  is  an  ever-present  theme  for  discussion.  In  any  case,  the  question  to  be  de- 
cided is  at  what  point  the  theory  shall  be  ignored  in  the  interest  of  clearness  and 
utility.  In  some  offices,  shade  lines  are  omitted  altogether.  The  following  ex- 
amples represent  the  more  general  practice  :  - 

(b)  Architect's  method  of  shade  lines.     Figs.  D,  E,  H,  and  K,  Fig.  105,  are 
shaded  according  to  the  architect's  method.     The  rectangular  objects,  Figs.  D  and 
E,  are  shaded  strictly  in  accordance  with  the  shading  of  the  cube  (A  and  C).     In  Z>, 
the  shade  lines  on  the  elevation  show  that  the  rectangle,  A,  represents  a  recess,  and 
the  rectangle,  B,  a  projecting  block.     In  E,  the  shade  lines  on  the  plan  indicate  the 
same  facts.     The  elevation  of  the  cylinder  (//),  is  not  shaded  wholly  in  accordance 
with  theory :  —  The  shade  elements,  ac  and  de,  do  not  coincide  with  the  contour 
(outside)  elements  of  the  cylinder ;  they  are  therefore  omitted,  and  no  element  is 
shaded.     The  shade  line  of  the  lower  base,  by  theory  extending  only  from  //  to  c, 
is  carried  clear  across  the  base,  and  no  part  of  the  upper  base  is  shaded.     The 
shade  line  of  the  plan  (K},  agrees  with  the  theory. 

(c)  Engineer  s  method  of  shade  lines.     In  this  method,  the  direction  of  the 
light  is  taken  the  same  for  all  views  and  sections  of  an  object.     The  direction  as- 
sumed is  downward  to  the  right,  and  all  views  are  shaded  similarly  to  the  elevation 
in  the  architect's  method.     The  shading  is  generally  done  by  some  arbitrary  rule, 
such  as  the  following  :  Shade  the  lower  and  right-hand  (sharp)  edges  of  objects,  and 
the  upper  and  left-hand  (sharp)  edges  of  holes  on  all  views  and  sections.    A  "  sharp  " 
edge  is  usually  taken  to  mean,  besides  an  actual  angle,  a  rounded  corner  where 
the  rounding  is  very  slight,  and  intended  only  for  a  finish.     Examples  :  — 

In  Figs,  /''and  G,  Fig.  105,  the  same  objects  as  in  D  and  E  are  shaded  accord- 
ing to  the  engineer's  method.  A  comparison  will  show  the  difference  between  the 
two  methods  of  shading. 

An  elevation,  a  section,  and  two  plans  of  a  hollow  cylinder  are  given  in  L.  The 
right-hand  contour  element  of  the  full  cylinder  is  not  shaded  because  it  is  not  a 
"sharp"  edge;  but,  where  the  section  is  taken,  both  the  right-hand  edge  of  the 
cylinder  and  the  left-hand  edge  of  the  hollow  are  shaded. 

The  object,  N,  as  it  is  bounded  entirely  by  curved  surfaces,  can  have  no  shade 
lines,  since  none  of  its  edges  is  "  sharp." 

The  object,  O,  is  bounded  by  flat  surfaces;  but  the  corners  are  slightly 
rounded  for  a  finish.  In  this  and  similar  cases,  by  theory,  the  shade  lines  would 
be  represented  by  the  fine  dash-and-dot  lines  shown  in  the  figure,  and  hence  the 
contour  would  not  be  shaded ;  in  practice,  however,  in  order  to  indicate  the  general 
(rectangular)  form  of  the  object,  the  edges  might  be  shaded. 


122 


OBJECT  DRAWING  —  SHADE  LINES — IRREGULAR  OBJECTS. 


(d )     The  following  rules  apply  to  both  systems. 

Details  which  fall  within  the  shadow  of  an  object  of  which  they  are  parts 
should  be  shaded  with  respect  to  their  own  light  and  shade,  unaffected  by  that  of 
the  larger  object.  Thus,  for  example,  each  link  of  the  bicycle  chain,  Fig.  106,  is 


Fig.   1 06. 


Fig.   107. 


shaded  according  to  the  arrows  shown,  whether  or  not  the  sprocket  wheel  is  in 
place.  The  rim  of  the  sprocket,  Fig.  107,  casts  a  shadow  on  some  of  the  teeth; 
but  all  of  the  teeth  are  shaded  individually  according  to  the  arrows. 

Dotted  lines,  representing  invisible  edges  of  an  object,  are  never  shaded. 

Finally,  if  there  is  any  question  as  to  whether  a  line  should  be  shaded  or  not 
it  is  usually  best  to  leave  it  unshaded. 

59.  Representation  of  Irregular  Objects;  Mixed  Rendering.  An  object  is 
said  to  be  irregular  when  it  cannot  be  readily  resolved  into  the  common  geometri- 
cal forms,  such  as  prisms,  cylinders,  spheres,  etc.  To  represent  an  irregular  object, 
it  is  necessary  to  locate  geometrically  its  essential  points,  which  are  then  connected 
by  lines  rendered,  according  to  convenience,  with  the  instruments,  by  means  of  the 
French  curve,  freehand,  or  by  a  combination  of  these  methods  (mixed  rendering). 

(a)  Methods  of  measuring  irregular  objects.  Either  of  the  following  methods 
may  be  used  in  locating  points  in  an  object.  (I.)  By  base  lines  and  offsets  (rec- 
tangular co-ordinates).  Assume  or  locate  a  base  line,  such  as  the  line  AB  of  the 
hook,  Fig.  G,  Plate  1 1 .  From  the  point  required  to  be  located,  as  X,  let  fall  a  per- 
pendicular or  offset,  as  KH,  to  the  base  line.  Locate  the  position  of  the  foot  of 
the  offset  by  measuring  along  the  base  line,  and  then  measure  the  length  of  the 
offset.  (II.)  By  triangulation.  To  locate  a  point,  as  D,  Fig.  E,  Plate  n,  meas- 
ure the  distances,  as  AD  and  BD,  from  each  end  of  any  line,  as  AB,  already  de- 
termined. 


Plate  II 

(Study   Plate    14) 


-4—       -^Fiq?H       MS 
~  ..^Tff^^^-T-zk 

T  KiiiiSE^    *  W- 

TTlTf^-^r-r^7      i  &Bk 


IUVW4     'f^ 
^^f^--1-1-^ 


The  dimensions  and  reference  letters  should  nof  appear  on  the  student's  drawing. 

("3) 


OBJECT  DRAWING — IRREGULAR  OBJECTS. 


125 


If  an  object  is  quite  irregular,  the  measuring  may  require  considerable  judg- 
ment and  ingenuity. 

(b)     A  three-pronged  hook.     To  illustrate  modes  of  procedure,  take  the  three- 
pronged  hook,  Fig.   H,  Plate  n,  also  shown  pictorially  in  Fig.  108.     The  hook  is 
symmetrical  with  respect  to  an  imaginary  plane  (central  plane)  which  passes  through 
the  highest  point,  D,  of  the  hook,  and 
contains  the  center  line  of  the  upper 
prong,  EGD.     The  imaginary  plane 
RSZ'  Y'    is    parallel  to    the   central 
plane;     and     the     imaginary     plane 
QRY'X',  representing  the  flat  sur- 
face of  the  hook,  Z,  produced,  is  per- 
pendicular to  plane  RSZ1  Y' . 

The  left-hand  vieiv,  Fig.  H,  Plate 
II.  This  is  a  view  seen  in  the  direc- 
tion of  the  arrow  Xy  Fig.  108,  per- 
pendicular to  the  imaginary  plane 
RSZ'  Y'  ;  hence  all  measurements 
for  this  view  must  be  taken  in  direc- 
tions parallel  to  the  plane  RSZ'  Y'. 
In  Fig.  1 08  the  central  plane  of  the 
hook  is  represented  by  the  triangles 
/',  2',  and  J.  The  total  height  of  the 
hook  is  equal  to  the  distance  CA', 
measured  along  the  edge  of  the  tri- 
angle /',  between  the  edge  CD  of  the 
triangle  J,  which  passes  through  the 
highest  point,  D,  of  the  hook,  and  the 
edge  A' B'  of  the  triangle  2> ',  which 
passes  through  a  point  midway  be-  Fig.  108. 

tween  the  lowest  points  A'"  and  A'v 

of  the  hook.     Point  A'"  is  located  by  the  base  line  obtained  with  the  triangle  /, 
and  the  offset  A  A'"  established  with  the  triangle  2. 

The  upper  prong,  since  it  is  parallel  to  plane  RSZ'  Y',  can  be  wholly  located  by 
means  of  points,  such  as  D,  determined  by  base  lines  and  offsets.  For  the  lower 
prongs,  K,  K',  a  different  method  must  be  adopted,  as  the  center  line  of  each 
prong  lies  in  a  plane  oblique  to  both  RSZ'  Y'  and  QR  Y'X ' .  The  upper  ends  of 
the  prongs,  being  comparatively  straight,  may  be  referred  to  the  center  lines  KL 
and  K' L' .  Viewed  in  the  direction  of  the  arrow  X,  the  nearer  prong  hides  the 


J 


126 


OBJECT  DRAWING — IRREGULAR  OBJECTS. 


further  one,  and,  therefore,  only  the  nearer  one  need  be  considered.  In  order  to 
locate  two  points  in  the  center  line,  GP,  a  means  must  be  found  for  projecting  the 
points  on  lines  which  are  parallel  to  the  plane  RSZ'  Y' .  The  following  method 
is  usually  sufficiently  accurate.  Looking  in  the  direction  of  the  arrow  X,  hold  any 
straight-edge  parallel  to  plane  RSZ'  V,  between  the  eye  and  the  hook,  so  that  the 
edge  will  cover  the  center  line.  Without  changing  the  position  of  the  eye  or  of  the 
straight-edge,  note  carefully,  either  by  sighting  or  by  squaring  out  with  the  triangle 
held  perpendicular  to  the  edge,  the  points  where  the  straight-edge  appears  to  cross 
any  two  lines  which  are  parallel  to  the  plane  RSZ'  Y' .  For  example,  points  so 
located  are  point  G  in  the  upper  prong,  and  point  H  in  the  offset  AB. 

The  curved  portion  of  the  prongs  may  be  determined  by  measuring  diameters, 
as  ^-|-"  and  -3-^",  Fig.  H,  Plate  1 1,  and  then  locating  the  position  of  these  diameters 
by  base  lines  and  offsets  as  shown. 

The  right-hand  view,  Fig.  H,  Plate  II.  This  is  a  view  seen  in  the  direction 
of  the  arrow  Y,  Fig.  108,  perpendicular  to  the  imaginary  plane  QRY'X ' ;  hence 
all  measurements  must  be  taken  in  lines  parallel  to  this  plane.  No  dimensions, 
however,  should  be  taken  which  can  be  projected  from  the  left-hand  view,  Fig.  H. 
For  example,  the  measurement  i^V',  Fig.  108,  giving  the  vertical  height  of  the 
lower  prong,  is  wholly  unnecessary,  as  this  height  is  already  determined  by  means  of 
the  center  line  JH,  in  the  left-hand  view  of  Fig.  H.  The  projection  of  the  angle, 

KPK' ,  Fig.  108,  made  by  the  center  lines 
of  the  straight  portions  of  the  lower 
prongs,  is  readily  determined  by  measuring 
the  lines  KK'  and  LL'  parallel  to  the 
plane,  QRY'X',  the  heights  of  which  are 
projected  from  the  left-hand  view,  Fig.  H. 
(c)  Turned  handles.  (Figs.  A,  B,  C, 
and  D,  Plate  n).  Use  the  center  line, 
AB,  of  the  handle  as  an  axis.  Measure 
diameters  at  a  sufficient  number  of  points 
to  determine  the  curvature  fully,  and  locate 
the  positions  of  these  diameters  by  meas- 
urements taken  parallel  to  the  axis.  En- 
deavor, as  far  as  possible,  to  find  places 
where  the  measurements  will  come  some 
even  division  on  the  scale,  for  both  the  dia- 
Fig.  109.  meters  and  the  distances  along  the  axis. 

In  addition  to   the  measurements  the  dis- 
tinctive characteristics  of  the  cmves  should  be  sketched  as  accurately  as  possible. 

(d)     Oblique  curves.     In  locating  the  points  of  a  curve  which  takes  a  diagonal 


OBJECT  DRAWING  —  IRREGULAR  OBJECTS  —  STUDY  PLATE  9.       127 

direction,  a  carpenter's  square  may  be  used  to  advantage.  Let  the  curves,  Fig. 
109,  represent  the  edges  of  the  legs  of  a  lathe  or  other  machine,  which  are  oblique 
to  a  vertical  surface  of  the  bed  or  table  portion  of  the  machine.  Place  one  edge  of 
the  square  on  the  floor,  with  the  other  edge  passing  through  the  highest  point  of 
the  left-hand  curve,  Fig.  109.  On  the  floor  draw  a  line  passing  through  the  foot 
of  the  vertical  edge  of  the  square  and  perpendicular  to  the  front  vertical  surface  of 
the  bed  of  the  machine.  Keeping  the  lower  end  of  the  vertical  edge  of  the  square 
always  in  the  line  on  the  floor,  move  the  square  forward  so  that  each  horizontal 
measurement,  as  B  and  C,  D  and  E,  etc.,  taken  at  convenient  heights,  A,  A.. ..A,  on 
the  square,  will  lie  in  a  vertical  plane  containing  the  face  of  the  square.  Also,  if  a 
plan  of  the  curve  is  required,  measure  on  the  floor  line  the  distance  the  square  is 
moved  forward  for  each  horizontal  measurement. 

(e)  It  is  sometimes  convenient  to  duplicate  a  given  curve  by  cutting  out  a 
template,  or  by  fitting  a  strip  of  sheet  lead  to  the  curve ;  the  curve  is  plotted  from 
the  template  or  lead  instead  of  measuring  the  original. 

(/)  In  concluding  this  subject,  it  should  be  pointed  out  that  the  drawing  of 
irregular  objects  is  a  final  test  of  skill  in  rendering,  especially  when  the  represen- 
tation depends  largely  on  freehand  methods.  The  common  objects  given  in  Plate 
1 1  are  typical  of  the  more  important  cases  which  are  likely  to  arise,  and  afford 
excellent  practice  in  mixed  rendering  and  in  the  management  of  complicated  di- 
mensions. Although  objects  requiring  treatment  similar  to  those  on  Plate  1 1  may 
be  met  with  only  occasionally  in  engineering  drawing,  yet,  when  such  occur,  they 
should  be  as  well  rendered  as  the  purely  instrumental  work ;  otherwise  the  ap- 
pearance of  the  whole  drawing  will  be  ruined. 

STUDY   PLATE  9. 

For  sketching;    the  rendering  of  dimensions  on  sketches;  collective  rendering;   reading 
drawings ;  lettering  and  dimensioning ;  speed. 

(a)  Sketching.     Place  Plate  12  from  20"  to  30"  from  the  eye  and  perpen- 
dicular to  the  line  of  sight.     On  a  single  page  of  the  sketch  book  (see  materials, 
page  2)  make  freehand  sketches  of  Figs.  A,  B,  C,  Z>,  and  E,  Plate  12  ;  the  sketches 
must  not  be  the  same  size  as  the  views  on  the  plate.     Use  an  H  to  3H  pencil,  and 
let  the  sketches  fill  the  page.     Read  Art.  50 ;  plan  the  general  position  of  the  sev- 
eral views  on  the  page ;  lay  in  the  masses  of  each  projection,  and  then  add  the  de- 
tails.    Place  on  the  sketch  all  measurements  and  data  given  on  Plate  12,  except 
when  marked  * ;  render  the  numerals  neatly  and  rapidly,  and  without  the  aid  of 
guide  lines. 

(b)  Collective  rendering.     It  is  required  to  make  a  pencil  drawing  of  the  hand- 
rail stud,  on  duplex  detail  paper,  for  a  tracing  the  size  of  which  is  to  be  1 4"  x  20",  with 
a  ruled  border  line  1 3"  x  19"  (-i"  margin).     Make  this  pencil  drawing  from  the  above 


128 


STUDY  PLATE   9. 


sketches  and  measurements,  but  locate  the  views  according  to  the  measurements 
given  on  the  Plate  1 2.  Lay  out  the  projections  as  follows  :  Draw  the  center  lines, 
NO,  PQ,  RS,  777,  and  VW,  Fig.  1 10.  Do  not  complete  one  projection  inde- 
pendently of  the  other  projections,  but,  within  practical  limits,  let  each  stage  of  the 

drawing  show  that  each  projection 
has  received  equal  attention.  Thus, 
for  example,  draw  the  circle  A  (K, 
Fig.  no),  and  project  the  width 
of  the  parts  A'  (Fig.  /)  and  A" 
(Fig.  H)  from  this  circle.  With 
the  compass  as  set  for  circle  A,  lay 
off  the  widths  of  the  part  A'"  (L) 
and  Aiv  (M).  Take  in  the  di- 
viders one-half  the  length  of  part 
A',  Fig.  J,  and  with  this  setting, 
measuring  from  the  center  lines, 
lay  off  the  lengths  of  A',  A",  A'", 
and  Aiv.  Draw  the  circle  B  (Fig. 
Z,) ;  from  B  project  B1 ',  B' ,  and 
with  the  compass  lay  off  the  width 
of  B'  at  B",  B",  and  B'",  B'". 
Draw  the  nut  E  (Fig.  Z),  accord- 
ing to  s,  Art.  45  ;  project  E'  (Fig. 
H] ;  make  E"  equal  to  E' .  Make 
the  width  of  the  nut  at  F  equal 
to  FG  (Fig.  L).  From  this  point 
the  several  views  may  be  treated 
more  in  detail. 

Draw  the    screw  threads  ac- 
cording to  c,  Art.  55. 


Fig.  1 10. 


(c)  The  tracing  ;  the  lettering  and  dimensioning.  Trace  the  drawing  accord- 
ing to  the  general  directions  for  tracing,  Study  Plate  i  (also  see  e,  Art.  44).  Make 
the  widths  of  line  according  to  those  of  the  lines  D — -J,  Fig.  5  5 .  Take  particular 
notice  of  the  arrangement,  on  Plate  1 2,  of  the  dimensions  and  data  relative  to  each 
view  of  the  object ;  then  stroke  render  all  dimensions  and  data,  not  marked  *, 
given  on  the  plate ;  make  the  style  and  size  of  the  numerals  and  letters  accord- 
ing to  Fig.  F,  Plate  5.  Balance  the  title  (b,  Art.  41)  on  the  vertical  center  line  of 
the  sheet ;  make  the  letters  of  the  title  according  to  the  style  and  heights  given  on 
Plate  12  ;  the  letters  should  be  drawn  (a,  Art.  41). 

Hand  in  the  sketch  book,  the  pencil  drawing,  and  the  tracing. 


Plate  12 

(Study   Plate  9) 


D/mens/ons  and  fettering  mar /fed  *  snou/d  not  appear  on  f/?e  s/uden/j 

(129) 


STUDY  PLATES   10  AND  u. 

STUDY   PLATE   10. 

For  sketching;  the  rendering  of  dimensions  on  sketches ;  arrangement;  collective  render- 
ing; reading  drawings;  lettering  and  dimensioning;  speed. 

(a)  Sketching.     Sketch  the  several  projections,  Plate   1 3  f  ;  proceed  strictly 
in  accordance  with  a,  Study  Plate  9,  but  let  the  sketches  fill  two  (or  three)  pages 
of  the  sketch  book  ;  the  sketches  must  be  larger  than  the  views  on  Plate  13.     Break 
the  screw  and  bring  the  parts  together  (b,  Art.    37).      Place  on  the  sketches  all 
measurements  and  data  given  on  the  plate,  except  when  marked  *. 

(b)  Arrangement.     On    any  spare  paper,  rule  a  border  line  i$"xig",  and 
design  an  arrangement  different  from  that  of  Plate  1 3,  but  which  shall  include  all  of 
the  views  there  given.     (See  Art.  51.) 

(c)  Collective  rendering.     Use  duplex  detail  paper  ;  rule  a  border  line   1 3"  x 
19";  and  make,  from  the  sketches  (see  a),  a  drawing  which  is  to  be  traced.     The 
views  must  be  located  according  to  the  student's  layout  (see  ft).     Draw  the  views 
with  respect  to  their  center  lines,  and  according  to  the  method  suggested  in  b, 
Study  Plate  9.     Draw  the  square  threaded  screw  according  to  Fig.  97. 

(d)  The  tracing ;  the  lettering  and  dimensioning.     The  size  of  the  tracing  is 
to  be  14"  x  20",  with  a  ruled  border  line  13"  x  19".    Proceed  according  to  the  gen- 
eral directions  for  tracing  Study  Plate  i  (also  see  e ,  Art.  44) .     Make  the  widths  of 
line  according  to  those  of  the  lines  D—J,  Fig.  5  5 .     Take  particular  notice  of  the 
arrangement,  on  Plate  1 3,  of  the  dimensions  and  data  relative  to  each  view  of  the 
object ;  then  stroke  render  all  dimensions  and  data,  not  marked  *,  given  on  the 
plate ;  make  the  style  and  size  of  the  letters  and  numerals  according  to  Fig.  F, 
Plate  5.     Balance  the  title  on  the  vertical  center  line  of  the  sheet ;  make  the  letters 
of  the  title  according  to  the  styles  and  heights  given  on  Plate   13  ;  the  letters 
should  be  drawn  (a,  Art.  41). 

Hand  in  the  sketch  book,  the  layout,  the  pencil  drawing,  and  the  tracing. 

STUDY  PLATE   11. 

For  the  assembling  of  details ;  speed. 

Make  an  assembly  drawing  of  the  head  of  the  clamp,  from  the  sketches,  af 
Study  Plate  10.  Locate  all  views,  and  draw  the  projections  of  the  block  of  the 
clamp  according  to  the  measurements  given  on  Plate  14. 

Use  Whatman's  cold-pressed  paper.  The  finished  sheet  is  to  be  14"  x  20", 
with  a  ruled  border  line  13"  x  19". 

Ink  the  drawing  carefully,  according  to  e,  Art.  44 ;  make  the  widths  of  line 
correspond  to  those  of  the  lines  D,  E,  F  and  G,  Fig.  55.  The  dimensions  and  data, 
not  marked  *,  should  be  stroke  rendered  ;  make  the  style  and  size  of  the  letters  and 

t  The  clamp  and  the  wrench  are  from  non-related  objects. 


132  STUDY  PLATES   n,   12  AND   13. 

numerals  according  to  Fig.  F,  Plate  5.  Balance  the  title  on  the  vertical  center  "line 
of  the  sheet ;  make  the  letters  of  the  title  according  to  the  styles  and  heights  given 
on  Plate  14 ;  the  letters  should  be  drawn  (a,  Art.  41). 

STUDY  PLATE   12. 

For  sketching ;  the  rendering  of  dimensions  on  sketches  ;  arrangement ;  collective  render- 
ing ;  reading  drawings  ;  lettering  and  dimensioning ;  speed. 

(a)  Sketching.     Sketch  the  details  of  the  hanger,  Plate  1 5  ;  proceed  strictly 
in  accordance  with  a,  Study  Plate  9,  but  let  the  sketches  fill  three  (or  four)  pages 
of  the  sketch  book ;  the  sketches  mtist  be  larger  than  the  views  on  Plate  1$.    Place 
on   the   sketches   all    measurements   and  data  given  on  the   plate,  except   when 
marked  *. 

(b)  Arrangement.     On  any  spare  paper  rule  a  border  line  i  3"  x  19",  and  de- 
sign an  arrangement  different  from  that  of  Plate  15,  but  which  shall  include  all  of 
the  views  there  given.     (See  Art.  5 1 .) 

(c)  Collective  rendering.     Use  duplex  detail  paper;  rule  a  border  line  I3"x 
19".     Make,  from  the  sketches  (see  a),  a  drawing  which  is  to  be  traced.     The 
views  must  be  located  according  to  the  student's  layout  (see  b}.     Draw  the  views 
with  respect  to  their  center  lines,  and  according  to  the  method  suggested  in  b, 
Study  Plate  9.     Draw  the  large  V-threaded  screw  according  to  e,  Art.  54. 

(d)  The  tracing ;  the  lettering  and  dimensioning.     The  size  of  the  tracing 
is  to  be  I4"x  20",  with  a  ruled  border  line  I3"x  19".     Proceed  according  to  the 
general  directions  for  tracing  Study  Plate  i  (also  see  e,  Art.  44).     Make  the  widths 
of  line  according  to  those  of  the  lines  D — -J,  Fig.  5  5 .     Take  particular  notice  of  the 
arrangement,  on  Plate  15,  of  the  dimensions  and  data  relative  to  each  view  of  the 
object ;  then  stroke  render  all  dimensions  and  data,  not  marked  *,  given  on  the 
plate ;  make  the  style  and  size  of  the  letters  and  numerals  according  to  Fig.  E, 
Plate  5.     Locate,  vertically,  the  lines  of  the  title  according  to  the  measurements 
given  on  the  plate,  but  center  the  title  between  the  edge  of  the  drawing  and  the 
ruled  border  line.     The  letters  of  the  title  should  be  drawn  (a,  Art.  41),  and  their 
style  copied  from  Plate  15. 

Hand  in  the  sketch  book,  the  layout,  the  pencil  drawing,  and  the  tracing. 

STUDY  PLATE  13. 

For  the  assembling  of  details  ;  speed. 

Use  Whatman's  cold-pressed  paper;  the  finished  sheet  is  to  be  I4"x2o", 
with  a  ruled  border  line  I3"x  19". 

Make  an  assembly  drawing  of  the  hanger  from  the  sketches,  a,  Study  Plate 
12.  Locate  the  drawings  according  to  the  measurements  given  on  Plate  16. 


Plate  13 

(Study  Plate  10) 


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(«37) 


Plate  16 

(Study   Plate  13) 


Dimensions  marked  *  should  nof  appear  on  the  students  drawing 

039) 


STUDY  PLATES  13  AND  14.  141 

Ink  the  drawing  carefully  according  to  e,  Art.  44 ;  make  the  widths  of  line  corre- 
spond to  those  of  the  lines  D,  E,  F,  and  G,  Fig.  5  5 .  Balance  the  title  on  the  verti- 
cal center  line  of  the  sheet ;  make  the  letters  of  the  title  according  to  the  style  and 
heights  given  on  Plate  16;  the  letters  should  be  drawn  (a,  Art.  41). 

STUDY   PLATE   14. 

For  practice  in  managing  complicated  measurements ;  mixed  rendering  in  pencil  and  in  ink. 

Use  Whatman's  hot-pressed  paper  ;  the  finished  sheet  is  to  be  14"  x  20",  with 
a  ruled  border  line  I3"x  19". 

I.     PENCILING.     Lay  out  the  border  line,  and  draw  the  several  figures  full 
size,  according  to  the  dimensions  given  on  Plate  1 1 . 

(a)  The  turned  handles  (Figs.  A,  B,   C,  and  D}.     Locate  and  draw,  of  in- 
definite length,  the  center  lines  AB.     Locate  the  lower  end,  and  lay  off  the  height 
of  the  handle.     On  the  center  or  base  line  lay  off  the  distances  which  locate  the 
positions  of  the  diameters ;  lay  off  the  diameters  on  lines  drawn  perpendicular  to 
the  base  line.     After  all  the  points  in  the  contour  of  the  handle  have  been  located, 
connect  them  by  a  lightly  rendered  freehand  line.     To  test  the  symmetry  of  the 
contour  of  each  handle,  place  tracing  paper  over  the  drawing,  rule  the  center  line, 
and  carefully  trace  one  side  of  the  contour.     Turn  the  tracing  paper  over,  make 
the  two  center  lines  coincide,  and  compare  the  semi-contour  on  the  tracing  paper 
with  the  underlying  semi-contour  of  the  original.     The  original  may  be  corrected 
by  means  of  the  tracing  paper,  but  the  points  located  by  scale  measurement  must 
not  be  changed. 

(b)  The  plane  handle  (Fig.  E}.     Locate  AB,  and,  using  this  line  as  a  base, 
triangulate  for  point  D  thus  :  With  radius  4^",  center  B,  describe  an  arc ;  with 
radius  4|",  center  A,  intersect  the  preceding  arc  in  point  D.     Draw  BD  and  AD. 
With  A£>  as  a.  base,  in  a  similar  manner  triangulate  for  point  C.     Locate  pointy, 
lying  in  AB,  \"  from  point  A.     Draw  the  base  line  CJ ' ;  locate  the  offsets  EF  and 
GH ' ;  measure  the  offsets,  and  connect  the  points  C,  F,  and  H.     Draw  a  horizontal 
line  Ty  above  AJ.     With  radius  ^",  center  in  a  line  drawn  parallel  to,  and  ^" 
distant  from  the  base  line  CJ,  draw  a  circular  arc  tangent  to  the  preceding  horizon- 
tal line  above  AJ.     Produce,  freehand,  the  line  already  drawn  through  points  F  and 
H,  to  give  a  smooth  curve  tangent  to  the  circular  arc.     Proceed   in  a  similar 
manner,  and,  in  general,  consider  the  longer  distances  first. 

(c)  The  saw  handle  (Fig.  F).     Locate  and  draw  the  vertical  line  AB.     Draw 
AC  perpendicular   to   AB ;  locate  point    C,  and  draw  CB.     With   CB  as  a  base 
line,  triangulate  for  point  D.     With  DC  as  a  base  line,  locate  points   G  and  H  by 
means  of  the  offsets  FG  and  EH.     Locate  point  R,  lying  in  GH  produced ;  locate 
point  S  in  line  CB,  and  draw  RS.     Draw  base  line  DB,  and  locate  point  /  by 


STUDY  PLATE  14. 

means  of  the  offset  KJ.  Locate  point  P  on  line  DG,  point  Q  on  line  BC,  and  draw 
base  line  PQ.  Locate  points  Fand  X  on  line  PQ,  point  Fby  means  of  the  offset 
WY,  and  draw  VY  and  YX.  Then,  proceeding  as  thus  suggested,  finish  the 
traverse  or  generalized  boundary  of  the  handle  as  a  whole ;  locate,  by  means  of 
base  lines  and  offsets,  the  more  important  points  in  the  boundary ;  and  finally,  lo- 
cate and  draw  the  curves  in  detail. 

(d)  The  hooks  and  the  cam  (Figs.  G,  H,  and  J).     The  drawings  of  these 
objects  should  be  plotted  according  to  the  preceding  methods. 

II.  INKING.  Make  the  width  of  line  equal  to  that  of  line  D,  Fig.  55.  All 
freehand  lines  and  lines  ruled  by  means  of  the  French  curve  should  be  so  skillfully 
rendered  that  they  will  be  uniform  in  appearance  with  the  straight  lines  made  with 
the  ruling  pen. 

(e)  Lettering.     Letter  "  Plate  14,"  your  name,  and  the  date.     The  dimen- 
sions and  all  other  lettering  may  be  omitted. 


CHAPTER    VIII. 

WORKING  DRAWINGS. 

60.  A  Working  Drawing  is  a  drawing,  made  in  accordance  with  engineering 
or  architectural   practice,*  which    presents  such  views  and  measurements  of  an 
object  as  will  enable  a  mechanic  to  make  the  object  wholly  from  the  drawing.     For 
complicated    structures,  such  as  buildings,   bridges,  and  machines,  two  kinds  of 
drawings  are  required,  namely:  (I.)  the  assembly  drawing  (see  Plate  16),  which 
shows  the  relative  positions  of  the  parts  in  the  completed  structure,  together  with 
its  most  general  dimensions;  and  (II.)  the  detail  drawings  (see  Plate  15),  which 
give  the  form,  arrangement,  and  dimensions  of  the  parts  of  an  object  taken  sepa- 
rately. 

If  a  drawing  is  made  from  an  existing  object,  the  data  consists  of  sketches  and 
measurements  from  the  object.  When  a  new  design  is  required  to  be  expressed, 
the  drawing  is  usually  worked  out  from  explanatory  sketches,  calculations,  and 
previous  drawings.  The  making  of  drawings  involving  data  of  the  latter  kind,  be- 
longs to  some  one  of  the  various  branches  of  engineering  or  architectural  construc- 
tion, and  therefore  lies  outside  the  scope  of  this  book. 

In  the  duplication  of  objects,  requiring  no  engineering  or  architectural  experi- 
ence, the  following  practice  should  be  adopted. 

61.  Sketching  the  Object.     (See  also  Art.  50.)     Sketch  only  such  views  of 
an  object,  or  a  part,  and  only  as  much  of  each  view,  as  are  necessary  to  make  the 
working  drawing.     Supplement  the  freehand  sketching  by  the  use  of  straight-edge 
and  compass  whenever  this  will  save  time.     Cultivate  the  habit  of  rendering  neatly 
and  legibly  all  sketches  and  dimensions,  as  frequently  in  office  practice  one  man 
makes  the  sketches,  while  another  makes  the  drawing  from  the  sketches. 

62.  Measuring  the  Object.     (See  also  Art.  50.)     Be  careful  not  to  omit  any 
essential  measurements ;  if  the  object  is  not  near  by,  an  omission  may  mean  both 
trouble  and  expense. 

(a)  Small,  nicely  machined  pieces  should  be  measured  with  a  micrometer 
caliper.  For  ordinary  work  a  two-foot  rule  and  machinist's  calipers  are  sufficient. 
Whenever  practicable,  take  as  the  base  lines  for  measurements  finished  edges  (as 

*  The  drawings  reproduced  in  Plates  12  to  1 6  were  made  primarily  to  illustrate  arrangement  and 
to  give  practice  in  reading  and  rendering.  Though  in  each  case  the  object  might  readily  be  made  from 
them,  they  are  not,  in  a  strictly  technical  sense,  working  drawings,  since  their  form,  as  will  presently  be 
seen,  is  not  wholly  in  accordance  with  office  practice. 

('43) 


144 


WORKING  DRAWINGS  —  MEASURING  THE  OBJECT. 


ft  f>  Fig.    J35)  °f   tne  object,  and,  if  possible,  take  all  measurements  from  the 
same  base  lines  (compare  Figs.  135  and   136). 

(b]     Circular  holes.     In  locating  a  hole,  do  not  attempt  to  measure  to  its 
center,  but  take  measurements  as  shown  in  the  following  examples.     Place  on  the 
sketch  the  measurements  just  as  they  are  taken,  although 
in  many  cases  this  is  not  the  way  they  should  appear  on 
the  working  drawing  (see  e,  Art.  65). 

A  single  hole.     (Fig.  1 1 1 .)     From  edge  A,  measure 
distances  AB  and  BC.     When  making  the  working  draw- 
ing, give  the  position  of  the  center  of  the  hole,  found  by 
adding  to  the  distance  AB  one-half  of  the  diameter  BC. 
Equally  spaced  holes  in  a  straight  line.     (Fig.  112.) 


JL. 


4- 


Fig.  iii. 


Lay  the  rule  along  the  center  line  AB,  measure  the  distance  between  correspond- 
ing edges,  as  A  and  B,  of  two  holes  at  a  considerable  distance  apart,  and  state  the 


Fig.  112. 

number  of  spaces  between  the  holes  in  question  —  in  this  case  6.  To  find  the 
distance  between  the  centers  of  adjacent  holes,  when  making  the  working  draw- 
ing, divide  AB  by  the  number  of  spaces  between  the  holes. 

Equally  spaced  holes  in  a  circle,  as,  for  example,  a  series  of  bolt  holes.  When 
the  number  of  holes  is  even  (Fig.  1 1 3),  measure  between  corresponding  points,  as 
A  and  B,  in  opposite  holes.  Re- 
cord the  number  of  holes  ;  if  nec- 
essary, one  hole  may  be  located 
with  respect  to  the  vertical  or 
the  horizontal  axis  of  the  piece. 
In  making  the  working  drawing, 
draw  the  circle  of  centers  (bolt 

circle)  with  a  radius  equal  to  one-  ^ 

half  of  AB.  and  space  the  circle 

T^  *  T  "*  * 

for  the  required  number  of  holes.  r«'  *  X3- 

When  the  number  of  holes  is  odd  (Fig.  1 14),  the  measurements  must  be  taken 
from  the  inner  or  outer  edge  of  the  piece,  according  to  which  is  the  smoother.  In 
the  case  shown  in  Fig.  114  the  inner  edge  of  the  piece  is  threaded,  and  therefore 
the  holes  are  located  from  the  outer  edge.  Measure  the  outside  diameter  D,  the 
distance  AB,  and  the  diameter  BC  of  a  hole.  When  making  the  working  draw- 


WORKING  DRAWINGS  —  PLANNING  THE  DRAWING.  145 

ing,  draw  the  bolt  circle  with  a  radius  equal  to  one-half  of  D,  minus  the  sum 
of  AB  and  one-half  of  BC,  and  space  the  circle  for  the  required  number  of  holes. 

If  the  holes  are  not  equally  spaced,  each  hole  may  need  to  be  located  sepa- 
rately.    No  general  rule  can  be  given. 

63.  Making  the  Drawing ;  General  Directions.     Ordinarily,  a  working  draw- 
ing may  be  said  to  include  the  layout  and  preliminary  drawing,  a  tracing,  and  a  blue 
print.     Both  the  tracing  and  the  blue  print  are  called  working  drawings.     The 
tracing  is  usually  retained  in  the  office,  while  the  blue  print  is  sent  away  for  shop 
or  other  outside  use. 

(a)  The  layout  should  be  made  directly  on  duplex  detail  or  a  similar  paper. 
After  the  scale  of  the  drawing,  the  number  and  arrangement  of  the  views,  and  the 
spaces  for  dimensions  and  title  have  been  decided  upon,  the  pencil  drawing  for  the 
tracing  should  be  continued  on  the  layout.      (See  Art.  52.) 

(b)  The  tracing.     (See  also  Art.  52.)     For  most  working  drawings  of  ma- 
chine construction  the  line  widths  D,  E — J,  Fig.  55,  are  appropriate.     In  draw- 
ings for  steel  construction,  since  many  of  the  lines  come  close  together,  it  may  be 
necessary  to  make  the  lines  somewhat  narrower,  both  for  clearness  and  to  prevent 
them  from  running  together.     It  must  be  borne  in  mind,  however,  that,  if  the  lines 
on  the  tracing  are  made  much  narrower  than  lines  D  — J,  Fig.  5  5,  they  are  very 
likely  to  be  weak  in  the  blue  print,  and  hence,  except  for  dimension  and  extension 
lines,  they  are  unsatisfactory. 

(c)  The  blue  prints.     The  process   of  obtaining  copies  by  blue  printing  is 
explained  in  Chapter  XI. 

64.  Planning  the  Drawing,     (a)     The  scale.     In  order  that  a  working  draw- 
ing may  best  serve  its  purpose,  it  is  necessary,  when  planning  it,  to  take  into  account 
not  only  the  immediate  facts  concerning  the  making  of  the  drawing  as  such,  but 
also  the  facts  connected  with  its  ultimate  use.     Thus,  for  example,  if  the  drawing 
is  to  be  used  at  the  bench  or  lathe,  it  should  not  be  of  a  size  which  will  be  un- 
wieldy, or  which  cannot  be  easily  scanned  by  the  mechanic.     On  the  other  hand, 
the  drawing  must  be  of  a  sufficiently  large  scale  to  enable  the  workman  to  read 
easily  all  of  its  parts  and  dimensions. 

(£)  The  number  of  vieivs.  In  the  interest  of  both  convenience  and  economy 
the  number  of  sheets  should  be  as  small  as  possible ;  that  is,  as  many  views  of  an 
object  should  be  placed  on  the  same  sheet  as  there  is  room  for  without  overcrowd- 
ing. Do  not  give  views,  or  parts  of  vietvs,  which  are  unnecessary.  The  views  se- 
lected should  be  such  as  will  best  set  forth  the  essential  characteristics  of  the 
object.  Thus,  the  interior  of  an  object  is  usually  represented  best  by  one  or  more 
sectio?ial  views  rather  than  by  dotted  lines,  which  are  more  likely  to  confuse  than 
to  explain.  For  example,  compare  the  projection,  Fig.  115,  having  all  invisible 


146 


WORKING  DRAWINGS  —  ARRANGEMENT  OF  THE  VIEWS,, 


lines  shown,  with  the  corresponding  projection,  Plate  16,  in  which  most  of  the  in- 
visible lines  are  omitted. 

(c)      The  arrangement  of  the  views.     In  planning  an  arrangement,  endeavor  to 
anticipate  the  probable  space  that  will  be  required  for  dimensions  placed  outside  of 

Avoid 


Fig.    115. 

the  views,  so  that  dimensions  belonging  to  different  views  shall  not  conflict.  (See 
Art.  65.)  In  all  drawings  of  machinery  place  the  views  according  to  third  angle 
projection*  This  gives  the  following  arrangement :  — 

Top  view. 

Left-hand  side  or  end  view.          Front  view.          Right-hand  side  or  end  view. 

Bottom  view. 

*  The  system  of  projection  most  generally  adopted  in  mechanical  engineering  is  that  of  the  third 
angle  of  descriptive  geometry,  although  first  angle  projection  is  also  followed  to  some  extent.  In  archi- 
tecture and  civil  engineering,  first  angle  projection  appears  to  be  generally  adopted;  that  is,  the  top 
view  is  placed  below  the  front  view,  the  left-hand  side  view  to  the  right  of  the  front  view,  and  the  right- 
hand  side  view  to  the  left  of  the  front  view. 

That  two  systems  of  projection  are  used  in  practice  is  unfortunate,  for  several  reasons.  When  a 
person  becomes  accustomed  to  one  angle,  it  is  more  or  less  confusing  to  read  drawings  made  in  the  other 
angle.  Then,  besides  this  inconvenience,  there  is  always  the  chance  for  costly  mistakes  in  the  shop,  result- 
ing from  reading  the  drawing  in  the  angle  other  than  the  one  intended  by  the  draftsman.  To  illustrate, 
take  a  case  which  occurred  just  at  the  time  of  writing.  A  former  student  in  architecture,  having  patented 
an  electric  street  railway  signal,  made  a  drawing  from  which  to  have  the  device  manufactured.  Naturally, 
as  an  architect,  he  made  his  drawing  in  the  first  angle.  When  the  lot  of  castings  was  delivered,  he  found 
that  certain  parts  which  should  be  on  particular  faces  of  certain  pieces  had  been  made  on  opposite  faces, 
and  that  the  castings  were  useless.  The  pattern  makers  read  his  drawing  in  the  third  angle  instead  of 
in  the  first;  hence  the  mistakes. 


WORKING  DRAWINGS — DIMENSIONING.  147 

65.  Dimensioning,  (a)  Necessary  dimensions.  In  order  to  dimension  a 
working  drawing  properly,  it  is  evidently  necessary  to  know  what  dimensions  should 
be  given.  This  requires  not  only  the  ability  to  discriminate  between  necessary  and 
unnecessary  measurements,  but  also  some  practical  knowledge  of  shop  construction, 
in  order  to  know  when,  and  what,  particular  measurements  may  be  needed  by  the 
mechanic.  As  a  simple  example,  take  the  case  of  a  hexagonal  bolt  head.  In 
forging  the  hexagonal  figure  of  the  head,  the  mechanic  can  easily  work  with  refer- 
ence to  its  short  diameter,  or  "  distance  between  the  flats  "  ;  whereas,  if  the  meas- 
urement of  the  diagonal  (long  diameter),  or  distance  between  corners,  is  given, 
he  must  figure  out  the  short  diameter,  or  work  at  a  disadvantage.  As  a  further 
illustration,  if  a  drilled  hole  is  dimensioned  according  to  the  directions  for  measur- 
ing (Art.  62),  that  is,  by  giving  its  diameter  and  the  distance  to  the  edge  of  the 
hole,  the  workman  must  figure  for  the  center,  since  he  must  know  at  what  point 
to  set  the  point  of  the  drill. 

If  unfamiliar  with  shop  requirements,  it  is  best,  when  dimensioning  a  working 
drawing,  to  give  all  essential  measurements  used  in  making  the  drawing. 

(b)  Forms  of  dimensions.     The  general  form  of   a  dimension  —  which  in- 
cludes the  numerals  expressing   the   measurement,  the  dimension  and  extension 
lines,  and  the  arrow  heads  — is  described  in  Art.  42. 

Because  of  the  general  use  in  shop  work  of  the  two-foot  rule,  dimensions  less 
than  two  feet  should  be  given  in  inches ;  if  greater  than  two  feet,  in  feet  and 
inches. 

(c)  General    system  of  placing   dimensions.     No    dimension  should  appear 
upside  down,  when  a  drawing  is  read  from  the  bottom  or  the  right-hand  side.     A 
satisfactory  system  of  placing  is  illustrated  by  the  several 

positions  of  the  diameter  dimension  shown  in  Fig.  1 1 6, 
which  will  be  found  convenient  for  reference  in  doubtful 
cases.  It  will  be  seen  that,  in  this  system,  all  dimensions 
read  from  the  bottom  of  the  sheet,  except  those  on  the  verti- 
cal line  AB,  which  read  from  the  right-hand  side  of  the  sheet. 

(d)  Position  of  dimensions  ;  clearness.     It  is  always 
important  to  place  a  dimension  in  such  a  position  that  it  may 
readily  be  seen  ;  its  connection  with  the  part  of  the  drawing 
to  which  it  refers  must  at  once  be  evident ;  and  it  must  not 
conflict  with  or  obscure  the  drawing.     To  secure  these  results 

may  require  considerable  ingenuity  and  judgment,  as  varying  conditions  must  be 
met  in  different  ways,  but  always  in  conformity  with  the  following  practice,  which 
must  be  regarded,  by  the  beginner,  as  invariable. 

On  assembly  drawings  give  only  the  most  general  dimensions,  such  as  overall 


148 


WORKING  DRAWINGS  —  DIMENSIONING. 


B 


Avoid 

JT  - 


1 


T.T 


1 1 

i._ 


:-§- 


dimensions  and  distances  between  centers.     Do  not  give  unnecessary  dimensions 
nor  repeat  a  dimension  on  the  same  drawing,  and  do  not  leave  any  calculating, 

however  simple,  to  be  done  by  the 
workman.  Do  not  fail  to  give  the 
totals  (overall  measurements)  of  inter- 
mediate measurements. 

Whenever  a  dimension  tends  to 
obscure  the  drawing,  or  if  the  actual 
place  of  measurement  will  be  more 
clearly  shown  thereby,  place  the  dimen- 
sion outside  of  the  view  by  means  of 
extension  lines  (B,  Fig.  117);  do  not, 
however,  place  the  dimension  so  far 
from  the  place  to  which  it  refers  that 
it  shall  appear  detached.  In  the  example  of  placing,  Fig.  1 18,  the  distance,  a,  be- 
tween dimensions,  and  between  a  dimension  and  an  edge  of  the  drawing,  is  made 
equal  to  the  distance,  b, 
used  for  the  height  of 
the  numerator  and  the  de- 
nominator. It  should  be 
understood,  however,  that 
the  distances  a  and  b  are 
not  to  be  measured ;  all 
placing  should  be  deter- 
mined by  eye. 


Fig.  117. 


Fig.  1 1 8. 


Avoid 


Extension  lines  must  always  be  drawn  parallel  (see  error,  Fig.  119),  and  at 
right  angles  (B,  Fig.  120)  to  the  direction   in  which  the   measurement  is  taken. 
(See  error,  A,  Fig.  120.)     A  dimension  line  must 
always  be  drawn  parallel  to  the  line  of  measurement. 
H  j — I  r1  Never  place  a  dimension  on  a  line  of  the  draw- 

ing, on  a  center  line  (A,  Fig.  117),  on  an  extension 
/'   ,\    /  ,)\       line,  or  on  a  dimension  line  of  another  dimension  (B, 
Fig.  121). 

Place  overall  dimensions  outside  of  detail  di- 
mensions, and  place  a  longer  dimension  outside  of  a 


Fie:.  1 20. 


Avoid 
Fig.  119. 

shorter  one  (B,  Fig.  117).  If  a  long  measurement  is  placed  between  the  drawing 
and  a  shorter  measurement  (A,  Fig.  117),  it  is  necessary  to  cross  the  dimension 
line  of  the  longer  measurement  by  the  extension  lines  of  the  shorter,  an  arrange- 
ment which  may  cause  confusion. 


WORKING  DRAWINGS  —  DIMENSIONING. 


149 


In  some  cases  greater  clearness  may  be  obtained  by  staggering  the  dimensions. 
This  consists,  A,  Fig.  122,  in  breaking  each  continuous  line  of  dimensions  (compare 
A  with  B,  Fig.    122)  or  in  breaking  up  symmetrical  columns 
of  dimensions,  as  the  diameters  in   Fig.    117,  by   placing   the 
dimensions  in  a  diagonal  column,  or   by   placing   alternate  di- 
mensions in  separate  columns.     Note.     As  the  system  A,  Fig. 
122,  is  not  in  common  use,  it  should  not  be  adopted  unless  au- 
thorized. 

(^)     Special  forms    of   dimensions.     When    the  space   in 
which  a  dimension  should  be  placed  is  too  small  to  take  the 


Fig.  121. 


dimension  without  interference  or  crowding,  the  following  forms  may  be  used :  — 
If  space  permits,  place  the  arrow  heads  as  usual,  but  place  the  dimension  at 


•13-4'V-  -H  4'-0"l«-  — »\  4'-0"l»- 

l          k — 8' — 0- — »j  J« — 6'—  0" — •>  l« — 6'— 0"- 


rre 


Fig.   122. 


Fig.  123. 


one  side  and  connected  with  the  dimension  line  by  a  narrow  freehand  line  (see  the 
left-hand  example,  A,  Fig.  123).  When  there  is  no  room  for  the  arrowheads, 
reverse  them  and  place  the  dimension  and  freehand  line  as  in  the  preceding  case 

(see  middle  example,  A,  Fig.  123).  Or  reverse 
the  arrow  heads  and  place  the  dimension  in  line 
with  the  arrow  heads,  omitting  or  using  dimen- 
sion lines  extending  outward  from  the  points  of 
the  arrows  according  to  preference  (see  the 
right-hand  example,  A,  Fig.  123).  A  combina- 
tion of  the  last  two  forms  is  shown  in  B,  Fig. 
123. 

A  comparison  of  confused  and  clear  dimen- 
sioning is  given  in  Fig.  124.  The  dimensions  given  in  A,  Fig.  124,  are  intended  for 
the  widths  of  the  projections,,  but  are  so  placed  that  they  give  the  widths  of  the 
spaces  between  the  projections  —  a  result  due  to  the  position  of  the  measurement 
relatively  to  the  arrow  heads,  and  the  omission  of  a  freehand  line  drawn  from  the 


?r  ^r  N2«ii  >* 

Avoid 


(III 


Correct 


Fig.  124. 


WORKING  DRAWINGS  —  DIMENSIONING. 


numerals  to  the  arrow  heads.     Compare  the  confused  arrangement,  A,  with  the 
clear  one,  B,  Fig.  1 24. 

Radii  of  circles.     If  there  is  sufficient  room,  a  radius  measurement  should  be 
placed  between  the  arc  and  its  center,  Fig.  125,  and  the  center  enclosed  in  a  free- 


Fig.  125.  Fig.  126.  Fig.  127.  Fig.  128. 

hand  circle  of  about  -Jg-"  diameter.     If  there  is  not  room  for  this,  the  center  should 
be  ignored,  the  dimensions  placed  according  to  Fig.    126,  and  the  letter  "  R"  or 
" Rad"  invariably  added.     In  the  case  of  concentric  arcs,  the  larger  radius  may  be 
reversed  (Fig.  126),  or  either  of  the  forms  shown  in  Fig.  127  may  be  used.     (The 
second  example  includes  the  radii  f  and  g.)     Do 
not  distort    the  form,    Fig.    126,   by   placing   the 
quantities  too  far  from  the  arrow  heads  (see  Fig. 
128). 

Do  not  give  the  radii  of  non-essential  curves 
such  as  those  representing  corners  rounded  for  a 
finish. 

Diameters  of  circles.  When  a  diameter  di- 
mension is  given  with  one  arrow  head  and  only  a 
portion  of  its  dimension  line,  Fig.  1 29,  whether  the 


W 

V 


Fig.  130. 


Fig.  129. 


whole  or  only  a  part  of  the  circle  be  shown,  the  dimension  must  invariably  be  fol- 
lowed by  "  D  "  or  "  Dia." 

Angle  measurements  should  be  given  as  shown  in  Fig.  1 30. 

Diameters  of  solids.  When  a  diameter  is  given  on  a  side  view  of  a  solid 
which  is  unaccompanied  by  a  view  showing  the  shape  of  the  cross  section  of  the 


DIA 


"  SQ 


«*-l"HEX  — »> 


"  OCT— *{ 


i 

^  1 

:  ) 

—  

3 

Fig.  131. 

solid,  the  dimension  should  include  an  abbreviation  descriptive  of  the  cross  section, 
as  follows:  "  D."  or  "  Dia."  (diameter);  "  Sq"  (square);  "Hex"  (hexagonal); 
"Oct."  (octagonal).  (See  Fig.  131.) 


WORKING  DRAWINGS  —  DIMENSIONING. 


In  a  composite  view,  where  a  partial  section  is  combined  with  an  outside  view, 
the  dimension  line  on  one  side  of  a  dimension  may  be  drawn  of  indefinite  length 
and  its  arrow  head  omitted,  Fig.    132,  which  shows 
that  the  measurement  reads  to  a  point  corresponding 
to  that  at  which  the  one  arrow  head  is  placed. 

Hollow  cylindrical  pieces,  of  material  which  is 


Fig.  132. 


Fig.  133- 


Circular  holes. 


thin  relatively  to  the  diameter  of  the  piece,  as  the 
shell  of  an  engine  boiler,  should  be  dimensioned  according  to  Fig.  133;  that  is, 
give  the  thickness  of  the  material  and  both  the  inside  and  the  outside  diameters 
of  the  piece. 

A  hole  must  be  dimensioned  by  giving  its  diameter  (B,  Fig. 
1 34)  and  the  distance  of  its  center  from  a  finished  edge 
of  the  piece  (A,  Fig.  134).  The  dimensions  taken  in 
measuring  the  object  (b,  Art.  62)  must  be  reduced  to 
bring  them  to  this  form.  When  there  are  several  holes, 
their  centers  should  be  located  as  shown  in  Fig.  135,  using 
the  same  two  edges  of  the  piece  as  base  lines  (see  error, 
Fig.  136). 

When  the  holes  are  all  of  the  same  diameter  and 


te —  B — * 


Fig.  134- 

Holes  in  a  straight  line. 
equally  spaced,  they  may  be  dimensioned  as  follows :  Locate  the  centers  of  the 
first  and  last  holes  in  the  line,  and  give  the  overall  dimension  between  these 
centers.  At  each  end  of  the  line,  dimension,  two  or  three  times,  the  distance 


3"- 


Avoid 


Fig.  135- 


Fig.  136. 


from  center  to  center  of  adjacent  holes,  also  two  or  three  diameters  of  the  holes ; 
but  omit  the  intermediate  dimensions  —  the  omission  will  indicate  that  the  spacing 
and  diameters,  respectively,  are  uniform  throughout. 

Holes  in  a  circle.     When  holes  are  equally  spaced  around  a  circle,  give  the 
diameter  of  the  circle  passing  through  the  centers  of  the  holes,  as  shown  at  A, 


152 


WORKING  DRAWINGS  —  CONVENTIONS. 


Figs.  137  and  138,  or  as  shown  at  B,  Fig.  138.  Calculate  the  diameter  according 
to  b,  Art.  62.  Give  also  the  diameter  of  one  or  two  of  the  holes  ;  this  will  indicate 
that  the  others  are  of  the  same  size.  No  other  dimensions  are  usually  necessary, 

since  equal  spacing  is  understood 
unless  otherwise  stated,  and  the 
number  of  holes,  unless  very  nu- 
merous, may  be  counted  from  the 
drawing. 

When  holes  in  a  circle  are  ir- 
regularly spaced,  or  not  all  of  the 
same  size,  all  necessary  measure- 
ments must  be  given. 

66.  Conventions.  (a)  Line 
conventions  are  given  in  Fig  55. 
When  a  sectional  and  an  outside  view  are  combined  (composite  view  or  projection), 
the  two  views  should  be  separated  by  a  dash-and-dot  line  (see  Plate  15). 

(b)  Shade  lines,  if  indicated,  should  be  treated  according  to  Art.  58. 

(c)  Shading  is  rarely  seen  in  working  drawings.     If  it  is  used,  the  light, 


Fig.  137- 


Fig.  138. 


Fig-  139- 

rapidly  rendered  examples  shown  in  Fig.  1 39  should  be  taken  as  a  guide,  rather 
than  the  examples  given  in  Fig.  D,  Plate  4. 

(d)  Materials.  The  conventions  shown  on  Plate  4  may  be  used  (see  Art. 
38).  The  graining,  Fig.  A,  Plate  4,  should  be  used  sparingly,  and  only  in  cases 
where  wood  might  be  mistaken  for  a  metal. 


WORKING  DRAWINGS  —  CONVENTIONS. 


'53 


(e)     Finished  surfaces.     When  a  surface  of  an  object  is  required  to  be  finished 
in  the  shop,  the  fact  is  indicated  by  means  of  a  lower-case  italic  /(Fig.  140).     The 
letter  should  never  be  placed  on  a  surface,  as  view  B,  Fig.  140, 
but  it  should  be  placed  on  a  line,  straight  or  curved,  which  is  an 
edge  view  of  the  surface.      Thus  the  three  f's  in  A,  Fig.  140, 
indicate  that  the  front,  top,  and  back  surfaces  of  the  block  are 
to  be  finished,   since  the  three  lines  on  which  the  letters  are 
placed  are  edge  views  of   the  surfaces  in  question.     Let  the 
cross  stroke  of  the  /  intersect  the  line  on  which  the  letter  is 


/' 

-r- 


Fig.  140. 


placed ;  if  the  line  is  horizontal,  the  cross  stroke  should  incline  at  45°.  When  all 
the  surfaces  of  an  object  are  to  be  finished,  the  /  should  not  be  used,  but  instead 
place  on  the  drawing  the  note,  "  Finish  all  over'' 

(/)  Screws  and  tapped  Jioles.  Any  of  the  con- 
ventions given  in  Figs.  98  and  99  is  appropriate.  In 
addition  to  the  convention  the  number  of  threads  to  an 
inch,  as  "  16  THD."  (A,  Fig.  141),  must  always  be  stated. 
To  save  time,  the  inclination  and  spacing  of  the  lines  of 
a  screw  thread  convention  should  be  determined  by  eye ; 
care  should  be  taken  that  the  opposite  ends  of  the 
longer  lines  shall  have  the  same  relative  positions  as  the 
points  of  a  thread,  Fig.  94,  but  do  not  attempt  to  repre- 
sent the  number  of  threads  to  an  inch. 

Additional  conventions  are  shown  in  Fig.  141. 
The  dotted  lines,  A,  indicate  that  a  piece  is  threaded  for 
the  distance  covered  by  the  lines  in  question.  The  con- 
vention B  is  used  to  represent  a  longitudinal  projection 
of  an  invisible  threaded  or  tapped  hole ;  the  same  con- 
vention is  also  used  for  the  screw  when  in  position. 
The  dotted  circle,  C,  shows  that  the  hole  is  threaded  ;  if 
the  hole  is  invisible,  both  circles  should  be  dotted.  In 
the  last  two  cases,  besides  the  thread  convention,  always 
give  the  diameter  of  the  tap  and  the  number  of  threads 
to  an  inch,  as  "f" — 16  TAP"  (B  and  C,  Fig.  141), 
unless  already  given  in  the  immediate  vicinity.  At  D 
is  shown  a  section  through  the  tapped  hole  which  re- 
ceives the  screw  A  ;  it  should  be  noticed  that  the  lines 
of  the  thread  convention  are  drawn  in  the  opposite  di- 
rection to  those  of  convention  A. 

When  a  section  is  taken  through  a  screw  and  the  tapped  hole  into  which  it 


i 

-   f—  16  TAP 

f— 16  TAP 


SECTION 

Fig.  141. 


154 


WORKING  DRAWINGS  —  LETTERING. 


fits,  none  of  the  thread  conventions  can  be  used  ;  it  is  therefore  necessary  to  draw 

the  sections  of  the  threads  (see  Fig.  142). 

67.  Letters  and  Numerals.  Plain  letters  and  nu- 
merals, such  as  those  given  in  Plate  5,  should  be  used. 
They  must  be  perfectly  legible,  and  for  speed,  if  under 
I"  in  height,  should  be  stroke  rendered  (Art.  40).  All 
letters  and  numerals  should  be  sufficiently  large  to  be 
easily  read  by  the  workman,  but  they  should  not  be  more 
conspicuous  than  the  drawings. 

As  vertical  numerals  take  less  space  laterally  than 
inclined  ones,  if  there  is  any  probability  of  crowding, 
only  vertical  numerals  should  be  used.  Comparing  A 
and  B,  Fig.  143,  it  will  be  seen  that  the  dimensions  in  B 
are  the  clearer;  even  when  the  size  of  the  inclined 
numerals  is  materially  reduced,  they  still  appear  more 


Fig.  142. 


crowded  in  the  narrower  spaces  than  the  vertical  (compare  B  and  C}. 

Do  not  omit  the  dash  between  feet  and  inches,  Fig.  144.  Do  not  make 
straight  top  3*3;  if  carelessly  made,  they  may  be  taken  for  5*5,  Fig. 
144.  Do  not  make  open-top  4's  ;  if  carelessly  made,  they  may  be 
taken  for  7's.  Always  make  the  dividing  line  of  a  fraction  hori- 
zontal ;  if  inclined,  it  may  lead  to  an  error  in  reading :  thus,  for 
example,  the  i  yg"  (Fig.  144)  might  easily  be  taken  for  \\" . 

68.  Titles.  Office  drawings  are  usually  filed  away  in  drawers  ; 
hence,  for  easy  reference,  the  title  must  be  placed  in  the  lower 
right-hand  corner  of  the  drawing.  An  expert  draftsman  can 
render  excellent  letters  up  to  |"  in  height  by  means  of  the  ruling 
pen  sharpened  for  lettering  (c,  Art.  40).  Several  pens  should  be  kept,  each 
sharpened  for  different  line  widths.  In  larger  letters  the  edges  of  the  outlines 


,,,.|   r,,| 
•-.» -+-/<? - 


Avoid  Avoid 

5  "  /  " 

f^  *   f^     ij  ^7       °¥  /          L^.  t^^ 

&       0.4  ->->*-)  *+         /  '/$ 

Fig.  144. 

should  be  stroke  rendered,  the  spaces  filled  in  with  the  pen,  and  the  letters  rapidly 
finished  freehand. 


CHAPTER    IX. 

PSEUDO-PICTORIAL  REPRESENTATION  —  ISOMETRIC   DRAWING. 

69.  Pseudo-pictorial  Representation.     This   form   of   drawing   includes  two 
general  systems  :  axonometric  projection,  which  includes  isometric  projection ;  and 
oblique  projection,  which  includes  cavalier  or  cabinet  projection.     In  either  of  these 
systems  an  object  is  represented  by  a  single  view  having  a  more  or  less  pictorial 
effect  —  a  fact  which  makes  these  methods  occasionally  convenient  in   describ- 
ing a  construction  to  persons  not  familiar  with  representation  by  plan  and  ele- 
vation. 

In  axonometric  projection  an  object  is  supposed  to  be  projected  on  a  plane, 
usually  vertical,  by  projectors  at  right  angles  to  the  plane ;  its  special  case  of  iso- 
metric projection  results  from  a  particular  position  of  the  object.  In  oblique  pro- 
jection an  object  is  supposed  to  be  projected  on  a  plane,  usually  vertical,  by 
parallel  projectors  not  at  right  angles  to  the  plane ;  its  special  case  of  cavalier  or 
cabinet  projection  results  when  the  projectors  make  an  angle  of  45°  with  the 
plane. 

Isometric  drawing  is  a  practical  modification  of  isometric  projection,  and  because 
of  its  greater  simplicity  and  more  general  usefulness  will  be  considered  first. 

70.  Isometric  Drawing.     All  rectangular  objects  are  bounded  by  three  sys- 
tems of  parallel  edges.     In  isometric  drawing,  lines  belonging  to  these  systems  are 
drawn  parallel,  respectively,  to  three  lines,  as  HK,  HJ,  and  HD,  Fig.  B,  Plate  17, 
known  as  the  isometric  axes.     One  axis  is  usually  taken  vertical,  the  other  two  at 
30°  with  the  horizontal. 

Isometric  drawings  are  usually  made  either  from  the  actual  object  or  from 
plans  and  elevations.  Let  Fig.  A,  Plate  17,  represent  the  plan  (C)  and  elevation 
(B)  of  a  cube  supposed  to  be  viewed  in  the  direction  of  the  arrow  5.  It  will  be 
seen  that,  in  the  isometric  (Fig.  B)  all  edges  of  the  object  which  make  45°  with 
the  vertical  plane  X  (Fig.  A)  are  drawn  parallel  and  at  30°  with  the  horizontal, 
and  that  the  vertical  edges  are  drawn  vertical.  The  lengths  of  the  edges  in  the 
isometric  drawing  are  made  equal  to  the  edges  in  the  object,  as  shown  by  the 
measurements  given  on  both  drawings. 

71.  Isometric  of  Rectangular  Solids,     (a)     A  cube  (Figs.  A  and  B,  Plate  If). 
Construction :    From  any  assumed  point,  D,  Fig.  B,  draw,  of  indefinite  lengths,  the 
vertical  line  DH,  and  the  lines  DE  and  DF,  making  angles  of  30°  with  the  hori- 

(155) 


156  ISOMETRIC  DRAWING. 

zontal.  From  point  D  lay  off  on  DH,  DE,  and  DF  the  measurement  (|")  given 
in  Fig.  A.  Draw,  at  30°  with  the  horizontal,  the  back  edges  EG  and  FG  of  the 
base ;  put  in  the  vertical  edges,  and  draw  the  top  of  the  cube. 

(b}  An  object  composed  of  rectangular  solids.  In  Fig.  C  is  given  the  plan 
(B}  and  elevation  (A)  of  a  model.  Consider,  as  in  the  projections  of  the  cube 
(Fig.  A],  that  the  object  is  placed  so  that  its  horizontal  edges  make  45°  with 
the  imaginary  vertical  plane  X,  Fig.  C.  Construction :  Starting  at  any  assumed 
point,  D,  Fig.  D,  and  reading  all  measurements  from  Fig.  C,  draw  the  part  FGE. 
A  projecting  piece,  as  dbg,  must  be  built  up  from  its  surface  of  contact ;  that  is, 
from  the  surface,  abcF,  common  to  both  pieces.  The  left-hand  piece :  Starting  at 
the  corner  F,  Fig.  D,  draw  the  surface  of  contact  Fabc,  its  edges  equal  to  Fabc, 
Fig.  C ;  draw  the  edges  ad,  be,  eg,  and  Ff,  and  connect  for  the  end  degf.  The 
right-hand  piece :  Lay  off  Gm,  Fig.  D,  equal  to  Gm  (\"}>  Fig.  C.  Draw  the  sur- 
face of  contact  mk/ij,  Fig.  D,  its  edges  equal  to  mkhj,  Fig.  C.  Draw  the  vertical 
edges  and  connect  for  the  top. 

(c)  A  rectangular  recess.  The  method  of  drawing  a  recess  is  illustrated  by 
the  mortise  in  the  piece  D,  Figs./"  and  K.  The  construction  is  begun  with  the 
rectangle  oprq,  and  completed  as  shown.  (Compare  the  similarly  lettered  lines  in 
Figs. /and  K.) 

72.  Non-isometric  Lines.  Curves  and  straight  lines  oblique  to  either  of  the 
three  systems  of  a  rectangular  object  must  be  located  by  means  of  rectangular 
co-ordinates  taken  parallel  to  two  (or  all  three)  of  the  systems.  Let  A  and  B, 
Fig.  E,  be  two  vertical  faces  of  a  cube,  and  C  a  horizontal  face,  upon  which  are 
drawn  oblique  straight  lines  and  curves  as  shown.  The  method  by  which  these 
oblique  lines  and  curves  would  be  drawn  in  isometric  is  illustrated  in  Fig.  G. 

(a)  The  lines  M  and  N,  Fig.  E.     As  the  line  M  intersects  the  two  edges, 
KH  and  FD,  of  the  cube,  make  Ka  and  Fb,  Fig.  G,  equal  to  the  distances  Ka  and 
Fb,  Fig.  F,  and  connect  the  points  a  and  b.      The  line  N.     The  extremity  d  of  the 
line,  Fig.  E,  is  located  by  the  co-ordinates  He  and  cd ;  the  extremity  f,  by  He  and 
ef.     The  isometric  of  these  co-ordinates  gives  the  position  of  the  points  d  and  /, 
Fig.  G. 

(b)  Polygons.     The  isometric  should  be  made  from  a  preliminary  drawing 
showing  the  true  shape  of  the  given  polygon.     Circumscribe  a  rectangle,  as  kmqp, 
C,  Fig.  E,  about  the  polygon ;  draw  the  isometric  of  the  circumscribing  rectangle, 
and  locate  the  corners  of  the  polygon  (see  Fig.  £). 

(c)  Plane  curves.     In  drawing  the  isometric  of  a  curve,  first  make  a  drawing 
showing  the  true  shape  of  the  curve,  and  draw  rectangular  co-ordinates  locating  a 
number  of  its  points.     In  the  case  of  a  circle  it  is  convenient  to  inscribe  and  cir- 
cumscribe parallel  squares,  the  sides  of  which  establish  the  co-ordinates  of  eight 


ISOMETRIC  DRAWING.  157 

points  in  the  circle ;  namely,  at  the  middle  points  of  the  outer  square  and  at  the 
corners  of  the  inner  square. 

Construction  of  the  vertical  circle,  B,  Fig.  E.  Draw  the  diagonals  and  diam- 
eters of  the  face  HJED,  Fig.  G.  On  a  diameter,  as  OP,  lay  off  the  distance,  as 
Od,  Fig.  E,  between  the  inscribed  and  circumscribed  squares.  Construct  the 
inscribed  square,  and  draw  the  curve  as  indicated  by  the  lettering  in  Figs.  E  and  G. 

The  horizontal  circle,  C,  Fig.  E.  The  construction  is  the  same  as  the  preced- 
ing, as  indicated  by  the  corresponding  letters  in  Figs.  E  and  G. 

(d)  Planes  and  solids.     The  faces  of  the  cube,  and  the  lines  drawn  on  them, 
Fig.  E,  are  repeated  in  Fig.  F.     It  will  be  seen,  however,  that  by  means  of  the 
additional  projections  D,  E,  and  G,  the  lines  drawn  on  the  faces,  Fig.  E,  become  in 
Fig.  F  the  projections  of  planes  and  solids.     An  isometric  drawing  of  the  planes 
(A],  cylinders  (B  and  C),  and  the  prism  (C)  would  be  begun  by  making  a  drawing 
precisely  the  same  as  Fig.  G.     The  lines  and  figures  drawn  on  the  surface  of  the 
cube,  Fig.  G,  are  the  lines  and  surfaces  of  contact  of  the  planes  and  solids,  Fig.  F, 
which  would  be  completed  in  the  isometric  as  follows  :  — 

The  planes,  A,  Fig.  F.  The  edges  a'g',  h'f ,  d'k' ,  and  f'm'  of  the  planes  M 
and  N  are  perpendicular  to  the  surface  of  the  cube,  and  hence  are  represented  in 
the  isometric,  Fig.  H,  by  lines  drawn  at  30°  and  equal  to  the  lengths  shown  in  D, 
Fig.  F. 

The  cylinders.  Each  cylinder  is  supposed  to  be  circumscribed  by  a  square 
prism  ;  the  base  of  the  prism  circumscribed  about  the  horizontal  cylinder  (B,  Fig. 
F)  is  represented  by  the  isometric  square,  acrp,  Fig.  H.  From  the  corner  a  of  the 
square,  Fig.  H,  draw  the  edge  aj  of  the  prism  equal  to  the  height,  g't' ,  of  the  cylin- 
der, Fig.  F.  Draw  the  isometric  of  the  outer  base  of  the  prism ;  inscribe  the 
isometric  circles,  and  draw  the  elements  of  the  cylinder  tangent  to  them.  The 
construction  is  similar  for  the  vertical  cylinder,  C,  Fig.  F. 

The  inclined  brace  F,  Fig.  K.  The  inclined  edges  of  the  brace  should  be 
obtained  by  connecting  the  ends  of  the  brace  (surfaces  of  contact),  which  are 
drawn  first  because  they  are  bounded  by  isometric  lines. 

(e)  Spheres  ;  double  curved  surfaces  of  revolution.     Make  a  preliminary  draw- 
ing, showing  the  true  size  and  figure  of  the  given  solid.     Take  a  series  of  parallel 
sections,  and  find  the  isometric  of  each.     A  line  tangent  to  these  sections  is  the 
required  curve.     An  isometric  drawing  of  a  sphere  is  a  circle,  but  its  diameter  is 
about  two-ninths  greater  than  the  diameter  of  the  given  sphere. 

(/)  An  approximate  method  for  drawing  the  isometric  of  a  circle,  by  the  use 
of  circular  arcs,  is  given  in  Fig.  145.  As  all  the  oblique  lines  are  drawn  at  either 
30°  or  60°,  the  construction  should  become  clear  by  inspection  of  the  figure. 
Turning  the  figure  so  as  to  bring  either  diameter,  2 — 2,  vertical,  will  give  the 


158 


ISOMETRIC  DRAWING  —  AXONOMETRIC  DRAWING. 


correct  positions  of  the  construction  lines  for  circles  lying  in  vertical  planes.     This 
method  is  usually  sufficiently  accurate,  except  in  the  case  of  very  large  circles. 


Fig.  145- 


Fig.  146. 


The  application  of  the  method  to  rounded  corners  is  shown  in  Fig.  146. 
When  AC  does  not  exceed  ^  inch,  however,  the  construction  at  A  becomes  so 
small  that  it  is  better  to  proceed  as  follows :  Make  distance  A'  B' ,  Fig.  146,  equal 
to  distance  C'D',  and  sketch  a  freehand  curve  through  points  C',  B' ,  and  £'. 

73.  Shade  Lines  in  Isometric  Drawing.    The   light  is  supposed  to  take  the 
direction    V,    Fig.    B,    Plate  1 7,  parallel  to   the  diagonal    KE   of   the  cube ;  the 
shadow  of  line  ab  is  represented  by  the  line  da',  parallel  to  the  diagonal  KJ.     The 
shade  lines  of  the  cube  comprise  the  boundary  LJHDF ;  the  practical  shade  lines 
of  an  isometric  drawing  are  those  which  can    be  determined  by  eye.     Another 
method  is  to  shade  all  lower  and  right-hand  (sharp)  edges  (see  c,  Art.  58). 

74.  Applications  of  Isometric  Drawing.     In  Figs.  J — P,  Plate  17,  are  shown 
practical  uses  of  isometric  drawing.     The  detail,  Fig.  M,  is  drawn  from  its  plan  and 
elevation  A  and  B,  Fig.  L.     The  detail  of  framing,  Figs.  O  and  P,  is  taken  from 
an  old-time  working  drawing  of  a  bridge  across  the  Saco  River  at  Hiram,  Me. 
While   the  type  of  construction   is  obsolete,  the  drawing  suggests  the  value  of 
isometric  in  representing  a  construction  not  easily  shown  in  plan  and  elevation  (see 
A  and  B,  Fig.  N). 

Perhaps  the  most  useful  and  general  application  of  isometric  is  to  describe 
details  of  building  construction  (see  Plate  18). 

75.  Axonometric  Drawing.     Isometric   drawing  is  a  special  case   of    axono- 
metric  drawing,  resulting  from  a  particular  choice  of  the  axes  (see  Art.  70)  taken 
to  represent  the  three  systems  of  parallel  edges  of   a  rectangular  object.     The 
general  case  of  axonometric  drawing  is  illustrated  by  the  cube  shown  in  Fig.  147. 
The  lines  AB,  AC,  and  AD  are  the  axonometric  axes.     One  axis,  AD,  is  usually 


Plate  17 


Fig-N 


(159) 


AXONOMETRIC    DRAWING OBLIQUE   PROJECTION. 


161 


Fig.  147. 


drawn  vertical,  and  made  equal  to  the  true  length  of  the  edge  of  the  object ;  the 
other  axes,  AB  and  AC,  are  drawn  at  any  convenient  angles,  and  their  lengths 
determined  by  descriptive  geometry.     In  general,  the  lengths  of  AB  and  AC  will 
not  be  equal  to  the  true  lengths  of  the  lines  of  the  ob- 
ject, as  in  isometric  drawing,  but  will  be  proportional  to 
these   lengths ;  these   proportions,    when  determined,  are 
known  as    the  scales  of  the  axes.     For   example,  if    AC 
were   found  to   equal  one-half   the  length    of  the   line  in 
the  object,  then  all  lines  in  the   system   parallel    to   AC 
must  be  drawn  one-half  of  their  true  lengths. 

For  practical  purposes  the  axes  may  be  arbitrarily 
assumed  in  such  positions,  and.  of  such  lengths,  as  will 
give  a  desirable  representation.  The  following  system 
agrees  closely  with  the  results  derived  by  descriptive  geom- 
etry, and  gives  a  satisfactory  appearance.  In  Fig.  147  draw  AD  vertical,  AB  at 
12°  with  the  horizontal,  and  AC  at  45°  with  the  horizontal.  Make  AD  and  AB 
each  equal  to  the  lines  of  the  object,  and  A C  equal  to  two-thirds  the  length  of  the 
line  of  the  object,  or  in  these  proportions  :  for  example,  if  AD  and  AB  are  laid  off 
from  the  scale  of  i^"  =  i  foot,  then  AC  should  be  laid  off  from  the  scale  of 
i"=  i  ft.  For  drawing  the  lines  at  12°  with  the  horizontal,  a  special  triangle  is 
convenient. 

Curves,  and  straight  lines  not  parallel  to  the  axonometric  axes  must  be  de- 
termined by  means  of  co-ordinates  parallel  to  the  axes.  The  methods  are  similar 
to  those  of  isometric  drawing,  except  that  the  scales  of  the  axes  must  always  be 
applied  to  the  co-ordinates. 

76.  Oblique  Projection.  A  cube  drawn  in  oblique  projection  is  shown  in 
Figs.  148  and  149.  In  this  system  one  axis,  AD,  is  taken  vertical,  another  axis, 


Fig.  148. 


Fig.  149. 


Fig.  150. 


AB,  is  taken  horizontal,  and  both  these  axes  are  laid  off  in  their  true  lengths. 
The  third  axis,  AC,  may  be  drawn  at  any  oblique  angle,  and  laid  off  to  any  desired 


162 


OBLIQUE  PROJECTION  —  STUDY  PLATE   15. 


proportion  of  its  true  length.  In  Figs.  148  and  149  the  line  ACis  made  equal  to 
its  true  length,  giving  the  special  case  of  oblique  projection  known  as  cavalier  or 
cabinet  projection. 

An  idea  of  the  general  effect  obtained  by  oblique  projection  may  be  gained 
from  Fig.  150.  (Compare  with  the  same  object  drawn  in  isometric,  Fig.  M,  Plate 
17.)  It  will  be  seen  that  the  drawing,  Fig.  150,  shows  the  true  shape  of  the  front 
and  back  faces  of  the  object.  The  lines  connecting  these  faces  are  drawn  at  45°, 
and  their  lengths  are  laid  off  to  a  scale  one-half  of  that  used  for  the  front  and  back 
faces. 

Oblique  projection  may  occasionally  be  useful ;  but,  as  the  principles  and 
methods  are  similar  to  those  of  isometric  drawing,  further  explanation  is  unnec- 
essary. 


r 

rt 

I/I                           ft] 

f*M                         K 

1 

I 

.9 

*p 
1 

1 

<P 

*     r 

t  —  f  

=± 

i_ 

&  —  I  U 

ll  w 

LW                                  \f 

i  =* 

40'-0"  Span 


Fig.  151. 


STUDY  PLATE  15. 

Isometric  drawing. 

Use  Whatman's  hot-pressed  paper.  The  size  of  the  sheet  is  to  be  io"x  14", 
with  a  ruled  border  line  9"  x  1 3".  Make  a  finished  isometric  drawing,  in  ink, 
scale  \" '  =  i  ft.,  of  the  roof  truss,  rafters,  etc.,  given  in  Fig.  151.  Place  the  point 
B,  Fig.  151,  !"  from  the  lower,  and  3"  from  the  right-hand  line  of  the  border; 
draw  the  line  AB  upward  to  the  left. 


Detail     •  of  •  Framing 


Plate  18 


Scale  %-\nch  -  I  fool"* 


IsomelTic  •  View  • 


Spike  Furring 

Snjd 

corner  poat*  ro 

nail  end  of  lart»i 

re- 


Raised   girr  4-"«  8%-^ 


Spike  plank 
againsr  girf 
hasten  ceiling 
Furring  ro. 


/I  furring  strip 
2.""  4-"  is  aer  on  in- 
ner edge  of  sill 
for  secure  nailing 
of  upper   Floor. 


ElevarTon-oF  Corner 


Copyr^bl-    I9,o    by 

From  Chandler's  Building   Construction   by  permission 
Size  of  the  Original    I4"x20!! 


(163) 


STUDY  PLATES   15  AND  16.  165 

Omit  invisible  lines,  and  the  bolts.  Put  in  shade  lines.  Do  not  give  the 
dimensions  (Fig.  151). 

Design  and  letter  on  the  drawing  the  title  "Roof  Truss,  Scale  \"  =i  ft."; 
also  letter  "Plate  15,"  your  name  and  the  date;  all  of  the  letters  are  to  be  drawn. 

STUDY  PLATE  16. 

Isometric  drawing. 

Use  Whatman's  hot-pressed  paper.  The  size  of  the  sheet  is  to  be  io"x  14", 
with  a  ruled  border  line  g"  x  1 3".  Make  an  isometric  drawing,  in  ink,  of  an  as- 
sembly of  the  clamp,  Fig.  87.  Take  with  the  dividers  the  distances  directly  from 
Plates  13  and  14. 

Before  beginning  the  drawing,  make  a  layout  to  determine  the  position  of  the 
drawing  on  the  sheet.  Show  the  bar  F,  and  the  glued  pieces  C,  C,  C,  C,  Fig.  87. 
Break  the  bar  and  the  piece  K,  in  order  that  each  shall  fall  within  the  ruled  border 
line.  Represent  the  thread  of  the  screw  according  to  convention  C,  Fig.  98,  but 
draw  the  lines  of  the  convention  curved,  and  parallel  to  the  edge  of  the  hole  through 
the  part  B,  Fig.  87.* 

In  the  binder,  G,  first  draw  it  as  if  square  in  cross  section,  and  then  shape  it 
freehand.  Treat  the  knobs  on  the  part  K  according  to  e,  Art.  72.  Omit  all  in- 
visible edges  ;  put  in  shade  lines. 

Design  and  letter  on  the  drawing  the  title  "  Cabinet  Maker's  Clamp"  ;  letter 
also  "  Plate  16,"  your  name  and  the  date  ;  all  of  the  letters  are  to  be  drawn. 

*  A  template  may  be  made  having  one  edge  straight,  and  the  curve  so  inclined  that  the  template 
may  be  moved  along  the  edge  of  the  T-square. 


CHAPTER   X. 

WASH   DRAWING. 

77.  A  Wash  is  a  mixture  of  India  ink  —  or  a  water  color  —  and  water,  applied 
with  a  brush. 

(a)  The  materials  for  wash  drawing.     Apart    from  the  considerable  skill 
necessary  to  manage  washes  successfully,  the  quality  of  a  result  depends  largely 
upon  the  quality  of  the  materials  used.     For  a  brief  course  of  study,  intended  merely 
to  give  the  practice  necessary  for  a  fairly  presentable  coloring  of  small  areas  — 
as  on  maps  and  surveyor's  plans  —  the  materials  given  on  page  2  may  be  used. 

If,  however,  the  subject  of  wash  drawing  is  approached  with  view  to  elaborate 
rendering  —  as  in  architectural  drawing,  see  Plate  22  —  only  the  best  materials 
should  be  used.  Get  the  best  quality  of  Japanese  ink ;  select  a  stick  which  dis- 
solves readily  under  the  moistened  finger,  and  in  which  the  dissolved  ink  tends  to 
a  brown  shade  rather  than  to  a  blue.  The  brown  sable  brushes  made  by  Winsor  and 
Newton,  while  expensive,  are  the  best ;  the  red  sable  of  the  same  make  are  the 
next  best.  Satisfactory  sizes  are  the  Nos.  6  and  n,  and  No.  4  of  the  extra  large 
series.  In  purchasing  a  brush,  selection  should  be  made  from  half  a  dozen  or 
more  after  trying  each,  as  follows  :  Thoroughly  saturate  the  brush  ;  then,  with  only 
enough  water  to  bring  the  hairs  to  a  point,  test  the  brush  by  drawing  it  briskly 
downward  and  across  the  finger  or  the  edge  of  a  water  glass.  Select  the  brush  in 
which  the  hairs  show  the  most  life,  and,  in  springing  to  place,  form  the  sharpest  and 
straightest  point. 

If  a  wash  is  applied  to  a  free  or  unstretched  light-weight  paper  (as  72  Ib. 
Whatman),  it  causes  the  paper  to  expand ;  and,  when  dry,  the  paper  will  be  more 
or  less  uneven  or  wrinkled.  Hence  there  should  be  used  a  very  heavy  paper  (not 
lighter  than  140  Ib.  Whatman) ;  a  Whatman  or  a  water-color  paper  mounted  on 
cardboard  ;  or  any  of  these  papers  made  into  a  water-color  block.  The  best  results 
are  obtained  on  stretched  paper.  % 

(b)  To  stretch  paper.     Place  the  paper  on  the  drawing  board,  with  the  better 
side  of  the  paper  uppermost.     Rule  a  pencil  line  parallel  to  and  i   inch  from  each 
edge  of  the  sheet.     At  each  corner  of  the  paper,  outside  of  the  ruled  line,  cut  out 
a  triangular  slip  of  the  paper,  as  shown  at   C,  D,  E,  and  F,  Fig.  152  (A).     Lay 
a  straight-edge  along  each  pencil  line,  and  bend  the  paper  until  it  stands  perpen- 
dicular to  the  drawing  board.     With  a  sponge  well   filled  with  water,    moisten 

(i  66) 


WASH  DRAWING  —  FLAT  WASHES.  167 

the  surface,  L,  taking  care  to  keep  the  upturned  margin  dry  and  not  to  abrade  the 
paper.  When  the  paper  has  become  quite  limp,  apply  to  «the  outer  surface  of  the 
margin,  G',  H',J',K>  (B),  a 
liquid  glue,  strong  paste,  or 
mucilage  ;  *  turn  down  the  mar- 
gin, A,  Fig.  152,  and  at  the 
same  time  pull  each  portion  -p. 

of  the  margin,  G,  H,  J,  and  K, 

toward  the  edge  of  the  board.  If  the  stretching  is  properly  done,  the  paper  will  dry 
out  perfectly  flat.  It  is  necessary,  however,  to  watch  the  work  until  the  adhesive  has 
set.  If  the  paper  dries  out  faster  than  the  adhesive,  the  contraction  of  the  paper 
will  cause  the  glued  margin  to  slide  away  from  the  edges  of  the  board,  and  the 
paper  will  dry  slack ;  hence,  if  the  adhesive  dries  but  slowly,  the  pulling  out  of  the 
glued  margin  should  be  repeated,  and  the  paper  again  moistened,  if  necessary.  On 
the  other  hand,  if  the  paper  is  very  wet  and  is  pulled  too  tight,  the  contraction  may 
cause  the  paper  to  tear,  or  may  warp  or  even  split  the  drawing  board. 

(c)  To  prepare  an  India  ink  ^vasJl.  Never  use  stale  ink,  but  grind  it  fresh  at 
each  exercise.  The  prepared  waterproof  liquid  inks  are  wholly  unsuitable  for  wash 
drawing.  As  the  ink  should  be  free  from  sediment,  it  is  best  to  grind  it  on  a  china 
slab.  See  that  the  slab  and  the  nest  of  saucers  are  clean  and  free  from  dust. 
Grind  a  reasonable  quantity  of  ink  —  which  need  not  be  so  thick  as  for  line  draw- 
ing —  to  be  used  as  a  first  supply  in  mixing  the  washes.  In  order  that  the  ink 
may  be  as  "  smooth  "  as  possible,  bear  down  but  lightly  on  the  stick,  and,  before  mix- 
ing a  wash,  let  the  ink  stand  a  few  minutes,  so  that  the  sediment  may  settle.  If  it 
is  required  that  a  wash  shall  match  a  given  wash  or  printed  area  (Plate  20),  the 
wash  must  be  tried  on-spare  paper  from  time  to  time,  when  preparing  it ;  the  shade 
or  value  must  not  be  judged  until  the  wash  is  thoroughly  dry.  To  mix  a  wash, 
half  fill  three  or  four  of  the  saucers  with  clear  water ;  add  to  the  water  in  each 
saucer  a  varying  quantity  of  ink,  taken  from  the  slab,  so  as  to  produce  several 
washes  of  different  values.  The  final  wash  should  then  be  obtained  by  modifying 
any  one  of  the  preceding  washes  by  admixture  from  the  others,  or  by  addition  of 
clear  water,  until  the  required  value  is  obtained.  It  is  difficult  to  obtain  a  required 
light  value  by  a  direct  mixture  of  dark  ink  and  water. 

78.  A  Flat  Wash.  A  wash  is  said  to  be  fiat  when  it  dries  out  to  a  uniform 
value,  and  is  free  from  a  clouded  appearance,  streaks,  and  spots.  A  direct  wash 
signifies  one  obtained  by  a  single  application  of  the  liquid  wash.  A  built  up  wash 
is  obtained  by  repeated  washes. 

*  The  liquid  glue  is  the  best,  but  it  softens  very  slowly  when  the  glued  paper  is  soaked  in  cleaning 
the  board. 


1 68 


WASH  DRAWING —  FLAT  WASHES. 


As  a  means  of  stating,  very  roughly,  the  amount  of  wash  a  brush  should  con- 
tain for  different  results,  let  the  expressions  a  "  full  brush  "  mean  one  holding  as 
much  of  the  wash  as  is  possible  without  dripping,  and  a  "  dry  brush  "  indicate  one 
holding  the  least  amount  which  will  permit  the  brush  to  transmit  wash  to  the 
paper. 

(a)  To  lay  a  direct  fiat  wash  on  an  unbroken  surface.  With  an  H  to  3H 
pencil,  rule  lightly  a  boundary  for  the  wash,  as  KADM,  Fig.  153.  Have  ready  a 

generous  supply  of  wash  and 
also  some  blotting  paper.  In- 
cline the  drawing  at  an  angle  of 
from  10°  to  15°  with  the  hori- 
zontal. With  the  largest  brush 
half -full,  starting  near  the  upper 
right-hand  corner,  C,  Fig.  153, 
and  carrying  the  brush  firmly 
and  accurately  along  the  ruled 
line,  DA,  lay  a  broad  strip  of 
the  wash,  C  to  B.  The  inclina- 
tion  of  the  paper  causes  the 
wash  to  settle  or  form  a  pool  (a 

portion  of  which  is  shown  at  GH}  along  the  lower  edge  of  the  strip,  and  the  man- 
agement of  this  pool  ("  flowing  the  wash  ")  is  the  principal  consideration  in  laying 
flat  washes.  Working  very  rapidly,  and  using  a  full  brush,  so  as  to  keep  the  pool 
as  full  as  possible  without  overflowing,  guide  the  pool  from  its  first  position,  FH,  to 
a  second  position,  a  portion  of  which  is  shown  at  KL  ;  this  should  be  done  with 
strokes  of  the  brush  perpendicular  to  the  line  FH.  The  pool  must  now  be  left  for 
an  instant  in  order  to  carry  the  wash, 
before  it  has  begun  to  dry,  accurately 
into  the  corners  A  and  D,  and  to  the  ruled 
border  at  AE  and  DJ ' ;  for  this  use  a  dry 
brush,  either  a  small  one,  or  the  one  al- 
ready in  use,  dried  on  the  blotting  paper. 
After  the  edges  of  the  wash  have  thus 
been  attended  to,  the  pool  must  be  ad- 
vanced with  the  full  brush,  the  edges 
again  managed  with  the  dry  brush,  and 
the  process  repeated  until  the  bottom 
ruled  line  is  reached.  As  this  line  is 


Fig.  154. 


approached,  the  wash  should  be  gradually  exhausted  from  the  brush  and  the  finish- 
ing strokes  should  be  made  with  the  dry  brush. 


WASH  DRAWING  —  FLAT  WASHES.  169 

(b]  To  lay  a  flat  wash  on  a  broken  surface.     Let  Fig.   154  represent  a  sur- 
face broken  up  by  the  rectangles  X — X,  which  are  not  to  receive  the  wash.     The 
process  is  the  same  as  that  described  in  the  preceding  paragraph,  except  that  the 
single  pool,  as  AB,  is  broken  up,  as  it  advances,  into  three  pools,  as  at  C,  D,  and  E, 
when  the  wash  must  be  treated  as  three  simultaneous  washes.     Along  the  line, 
FG,  of  the  lower  edges  of  the  rectangles,  the  pools  C,  D,  and  E  are  again  joined  to 
form  a  single  pool,  as  HJ.     With  the  attention  divided  between  the  alternate  use 
of  the  wet  and  the  dry  brush,  the  keeping  of  all  advancing  edges  wet,  and  the 
accurate  following  of  the  ruled  lines,  it  is  evident  that  considerable  dexterity  is 
necessary,  and  that  the  draftsman  must  work  rapidly. 

(c)  Precautions  necessary  to  secure  aflat  wash.     In  order  that  a  wash  shall 
dry  out  flat,  it  is  necessary  that  the  value  of  the  wash  shall  not  vary ;  therefore,  as 
a  wash  quickly  settles  in  the  saucer,  it  must  be  remembered  to  stir  up  the  wash 
each  time  it  is  applied  to  the  drawing.      Moreover,  it  is  necessary  that  the  wash 
shall  be  fed  uniformly  into  the  pool ;  that  is,  in  floating  a  wash,  the  brush  must 
hold  the  same  amount  each  time  it  is  applied  to  the  paper.     The  results  of  a  non- 
observance  of  the  latter  requirement,  and  of  working  too  slowly,  are  shown  in  Fig. 
F,  Plate  19.     In  making  the  drawing  for  this  cut,  the  wash  lay  flat  while  handled 
at  a  proper  speed  ;  but  on  slower  working  the  slight  cloudiness,  at  DE,  appeared. 
At  FG  the  wash  was    allowed  to  become  almost  dry,  hence   the   streak.     The 
streak  at  HJ  resulted  from  an  excessive  pool  at  KLt  which  caused  the  wash  to 
flow  back  into  the  partially  dried  portion  between  FG  and  KL.     The  spot  at  the 
corner  N  resulted  from  carrying  the  pool  into  the  corner,  instead  of  exhausting  the 
wash,  as  described  above. 

A  wash  tends  to  dry  out  in  a  hard  edge,  as  at  BC  and  CE ;  and  hardness  is 
increased  if  the  wash  collects  in  a  groove  made  by  using  too  hard  a  pencil  or  by 
bearing  down  on  the  pencil.  Hard  edges  may  be  avoided,  as  at  GJt  by  slightly 
thinning  the  wash,  at  its  very  edge,  with  clear  water,  used  in  a  dry  brush.  A  soft 
edge  may  also  be  obtained  by  building  up  a  wash  with  two  washes,  and  keeping  the 
boundary  of  the  second  wash  —  without  the  aid  of  a  ruled  line  —  a  trifle  inside 
the  boundary  of  the  first  (see  the  edges  AB  and  AD}. 

Before  laying  a  wash,  see  that  the  paper  is  clean ;  if  at  all  soiled,  it  should  be 
washed  with  clean  water  applied  with  a  soft  sponge.  The  use  of  a  rubber  is  likely 
to  injure  the  surface.  A  direct  wash  is  likely  to  work  better  if  the  surface  is  first 
gone  over  with  a  very  light  wash  of  the  India  ink,  or  with  water  containing  a  trace 
of  yellow  ochre.  A  wash  is  more  likely  to  be  flat  if  the  paper  can  be  kept  slightly 
damp  (not  moist). 

In  laying  in  a  narrow  stripe  (see  Plate  20),  the  wash  should  be  managed  as 
described  for  a  flat  wash,  but  the  pool  should  contain  less  of  the  wash.  For  very 


170  WASH  DRAWING  —  GRADED  WASHES. 

large  areas,  a  foot  square  or  more,  a  camel-hair  sky  brush  may  be  used,  but  the 
edges  should  be  managed  with  the  sable  brush. 

79.  Graded  Values.     The  light  and  shade  of  a  surface  may  be  expressed  by 
means  of  a  series  of  graded  flat  washes,  or  by  grading  a  direct  wash. 

(a)  To    lay  a   wash    of    uniform    gradation,    by    means   of   fiat    washes. 
Let  it  be  required  to  obtain  a  gradation  with  four  washes,  as  shown  by  A — D,  Fig. 

A,  Plate  19.     Rule,  lightly,  pencil   lines   representing   the   edges    of   the   several 
washes,  D,  Fig.  A.     Repeat  these  lines  several  times  on  spare  paper  to  be  used 
in   the  trials  necessary  to  determine    the  value  of   the   dry   washes.     Prepare   a 
wash   which   shall   give  the  lightest  value,  Fig.  A  ;    then  a  second  wash  which, 
when  applied  over  the  first  one,  will  give  the  next  value,  Fig.  B  ;  and  so  on.     Lay 
the   washes  in  the  order  of  the  values,  beginning  with  the  lightest,  as  shown  in 
A — D,  Fig.  A .     The  edges  will  be  somewhat  softer  if  the  washes  are  laid  in  the 
reverse   order ;  that  is,   beginning  with   the   darkest   value,  and  overlapping   the 
subsequent  washes.     Each  wash  should  be  thoroughly  dry  before  the  next  one  is 
applied. 

The  modeling  of  a  cylinder  by  using  four  flat  washes  is  shown  in  A — D,  Fig 

B,  Plate   19.     The  shading  of  a  sphere,  by  the  same  method,  is  given  in  B — E, 
Fig.  C ;  the  outlines  for  the  washes  may  be  drawn  as  indicated  in  A. 

A  water  line  (see  Plate  21)  should  be  begun  with  the  lightest  wash,  A,  Fig.  D, 
Plate  19.  As  the  width  of  the  wash  must  not  vary,  the  edges  may  merge  in  the 
narrow  places,  thus  giving  a  continuous  wash,  as  between  the  shore  lines  on  the  right- 
hand  side  of  A.  In  the  second  wash,  Bt  Fig.  D,  the  edges  merge  only  between  the 
island  and  the  shore  line. 

The  drawing  of  the  hook,  Fig.  G,  was  built  up  with  a  considerable  number  of 
flat  washes  applied  without  the  aid  of  pencil  outlines. 

(b)  To  lay  a  graded,  direct  wash.     This  gradation,  E,  Fig.  A,  Plate  19,  may 
be  effected  by  beginning  the  wash  with  the  darkest  value,  and  then  gradually  dilut- 
ing the  pool  of  wash,  as  it  advances,  by  adding  clear  water.     A  better  way  is  to 
prepare  several  washes  of  graded  values ;  begin  with  the  darkest,  and  lighten  the 
advancing  pool  with  the  prepared  washes  taken  in  the  order  of  their  values.     Clear 
water  should  also  be  at  hand  to  modify  the  advancing  pool,  if  necessary. 

(c)  A  built-up  graded  wash.     Proceed  as  in  the  previous  paragraph,  but  use 
much  lighter  washes.     In  H,  Fig.  B,  is  shown  a  cylinder  shaded  by  this  method ; 
the  several  stages  are  indicated  in  E,  F,  and  G. 

80.  Methods  of  Correcting  a  Wash  Drawing,     (a)      Washing.     Minor  spots 
and  streaks  may  be  partially  eliminated  by  washing  with  clean  water  applied  with 
the  brush.     The  part  should  be  thoroughly  soaked  and  scrubbed  with  the  brush, 
and  the  water  then  removed  with  blotting  paper ;  in  medium  to  light  washes  a 


Plate  19 


Fig.  A. 


Fig.  D. 


Avoid 


Fig.  F. 


Fig.  G. 


(170 


WASH  DRAWING — METHODS  OF  CORRECTION.  173 

result  may  not  be  perceptible  until  the  process  has  been  repeated  several  times. 
In  order  to  make  radical  corrections,  it  is  necessary  to  sponge  the  whole  drawing, 
although  a  part  of  the  drawing,  if  isolated  by  clear  paper,  may  be  so  treated.  All 
traces  of  the  wash  must  be  removed  from  the  paper  by  repeated  applications  of 
clean  water,  as  the  slightest  discoloration  of  the  water  will  stain  the  paper.  If  the 
whole  drawing  is  to  be  washed,  it  may  be  placed  directly  under  the  water  faucet. 
The  sponge  must  be  a  soft  one,  and  used  lightly,  so  as  not  to  rub  up  the  surface  of 
the  paper. 

(£)  Stippling.  This  is  the  modifying  of  a  dry  wash  by  the  placing  of  small 
spots  of  liquid  wash  applied  with  the  point  of  a  dry  brush.  To  illustrate  the  proc- 
ess, let  it  be  required  to  build  up  a  value  EF,  Fig.  E,  Plate  19,  wholly  by  stip- 
pling. The  paper  is  first  spotted  with  the  point  of  the  dry  brush,  as  shown  at  AB. 
The  spots  of  clear  paper  at  AB  are  broken  up  by  additional  touches,  as  at  CD, 
but  without  overlapping  the  first  spots.  The  clear  paper  is  further  eliminated  by 
a  third  spotting,  as  at  GHt  with  smaller  touches  of  the  wash,  and  the  process  con- 
tinued until  a  required  value,  EF,  is  produced.  Stippling  consumes  much  time, 
and  considerable  practice  is  necessary  in  order  to  judge  correctly  the  value  of  the 
liquid  wash  used  in  the  spotting. 

Stippling  is  permissible  only  when  it  may  be  the  means  of  saving  considerable 
time  in  redrawing.  Brush  washing  with  pure  water  and  stippling  may  be  alter- 
nated. 

81.  Miscellaneous  Notes,  (a)  Ink  lines.  In  a  wash  drawing  proper  —  such 
as  the  architectural  drawing.  Plate  22 — all  edges  which  would  be  represented  by 
lines  in  an  outline  drawing  are  represented  by  the  value  differences  of  the  washes. 
Such  edges  must  never  be  further  defined  by  ruled  lines  in  black  ink,  although  an 
edge  may  be  accented,  occasionally,  by  a  line  of  wash  applied  with  the  ruling  pen. 
In  elaborate  engineering  drawings,  maps,  and  plans,  on  which  flat  washes  are  used, 
the  inking  should  follow  the  laying  of  the  washes  ;  but,  in  working  drawings  and 
rush  work,  washes  may  be  applied  after  the  inking,  providing  the  lines  are  drawn 
with  waterproof  ink. 

Chinese  white,  a  pigment  of  value  in  making  pictorial  illustrations,  should  not 
be  used  on  washes  in  architectural  or  engineering  drawing. 

An  ink  line  should  never  be  drawn  around  the  edge  of  a  cast  shadow. 

(b)  Care  of  the  brushes.  The  brushes  should  be  washed  out  thoroughly  after 
use,  the  hairs  brought  to  a  straight  point,  and  the  brushes  kept  in  a  brush  holder. 
If  a  brush  is  laid  in  a  drawer,  care  must  be  taken  that  the  point  does  not  come  in 
contact  with  anything ;  a  point  which  dries  bent  is  usually  spoiled.  India  ink 
ground  black  for  line  work  should  never  be  used  in  a  wash  brush,  as  it  is  difficult 
to  remove  all  traces  of  the  ink. 


174 


STUDY  PLATE   17. 


STUDY    PLATE    17. 

Flat  and  graded  washes. 

Use  Whatman's  cold-pressed  paper.  The  size  of  the  finished  plate  is  to  be 
io"x  14",  with  a  ruled  border  line  8"  x  12".  Stretch  the  paper  (b,  Art.  77),  and 
rule  lightly  with  an  H  pencil  the  boundaries  of  the  washes,  Plate  20,  according  to 
the  measurements  given  in  Fig.  155.  Any  erasure  in  connection  with  the  pencil- 
ing should  be  done  lightly  with  a  velvet  rubber,  so  as  not  to  injure  the  surface  of 
the  paper. 

It  is  required  to  lay  flat  and  graded  India  ink  washes  (Arts.  78  and  79) 
of  the  values  shown  on  the  plate.  Take  the  areas  in  the  order  of  their  ar- 


(0100 


Fig.  B 


Fig.A 


-too 

( 

j 

_ 

1                 I           Jfc 

* 

* 

Fig.C 


Fig.  D 


Fig.  K 


Fig-  155- 

rangement.  The  values,  Figs.  A,  B,  E,  F,  H,  and  K,  must  be  obtained  with  a* 
single  wash  ;  not  more  than  two  washes  may  be  used  for  Fig.  D,  and  not  more  than 
three  washes  for  Fig.  C ' ;  the  number  of  washes  for  Figs.  G  and  J  is  not  limited. 
Stippling  must  not  be  used. 

Ink  only  the  ruled  border  line  of  the  plate,  and  the  lettering  "Plate  17,"  your 
name,  and  the  date  (drawn  letters). 


o  ^ 

CVJ    4) 

"15 
0  E 

2  f 

0-  £ 


075) 


STUDY  PLATES  18,  19,  20,  AND  21.  177 

STUDY  PLATE   18. 

Modeling  by  graded  washes. 

Use  Whatman's  cold-pressed  paper,  stretched.  The  finished  plate  is  to  be 
10"  x  14",  with  a  ruled  border  line  8"  x  12" '. 

It  is  required  to  arrange  and  shade  six  figures  similar  to  B,  D,  F,  H,Jt  and  L, 
Fig.  156  (also  see  Plate  21),  changing  the  sizes  and  the  proportions  so  as  to  fill  the 
sheet  satisfactorily.  Make  a  layout  for  the  arrangement,  and  then  lightly  draw  the 
figures  with  an  H  pencil.  Model  the  forms  with  graded  washes;  take  Plate  21  as 
a  general  guide,  but  keep  the  darkest  value  in  each  figure  lighter  than  that  on  the 
plate. 

Ink  only  the  ruled  border  line  of  the  plate,  and  the  lettering  "  Plate  18,"  your 
name,  and  the  date  (drawn  letters). 


STUDY    PLATE    19. 

Modeling  by  flat  washes. 

Pi-oceed  as  in  Study  Plate  1 8,  but  let  the  modeling  be  done  with  graded  fiat 
washes  (see  Figs.  A,  C,  E,  G,  and  K}. 


STUDY  PLATE  20. 

Modeling  and  water  lines  by  graded  washes. 

Use  Whatman's  cold-pressed  paper,  stretched.  The  finished  plate  is  to  be 
10"  x  14",  with  a  ruled  border  line  8"  x  12". 

It  is  required  to  arrange  and  shade  three  figures  similar  to  M,  O,  and  Q, 
Fig.  156  (also  see  Plate  21),  changing  the  sizes  and  proportions  so  as  to  fill  the 
sheet  satisfactorily.  Make  a  layout  for  the  arrangement,  and  then  lightly  draw 
the  figures  with  an  H  pencil.  Render  the  pipe  and  the  water  lines  with  graded 
washes;  take  Plate  21  as  a  general  guide,  but  keep  the  darkest  value  in  each 
figure  lighter  than  that  on  the  plate. 

Ink  only  the  ruled  border  line  of  the  plate,  and  the  lettering  "  Plate  20,"  your 
name,  and  the  date  (drawn  letters). 


STUDY  PLATE  21. 

Modeling  and  water  lines  by  flat  washes. 

Proceed  as  in  Study  Plate  20,  but  let  the  pipe  and  the  water  lines  be  ren- 
dered vaflat  instead  of  graded  washes  (see  Figs.  TV  and  />). 


I78 


STUDY  PLATE  22. 


STUDY  PLATE  22. 

Modeling  and  water  lines  by  flat  and  graded  washes. 

Use  Whatman's  cold-pressed  paper.  The  size  of  the  finished  plate  is  to  be 
io"x  14",  with  a  ruled  border  line  8"  x  12".  Stretch  the  paper,  and  lay  out  the 
figures,  Plate  21,  according  to  the  measurements  given  in  Fig.  156. 


Fig.  156. 

It  is  required  to  make  an  accurate  copy  of  Plate  21,  for  values,  and  treatment 
(see  Arts.  78  and  79). 

Ink  only  the  ruled  border  line  of  the  plate,  and  the  lettering  "  Plate  22,"  your 
name,  and  the  date  (drawn  letters). 


Plate  22 


ROME 


FORVM 

DE-TRAlAN 


ENTABLEMENT 
DE-LA-BASEIOVE  * 


JBL  JB  ^mr  .jg  .j«../jBr..jBt'.3it\ja  JH  jg  ;?!  .JH.:JH..JH  a 


FROM    THE    WASH    DRAWING    BY   A.  TOURNAIRE. 

The  size  of  the  original  is  24  x  38  inches. 

(181) 


CHAPTER   XL 

MECHANICAL   COPYING  — THE  BLUE-PRINT   PROCESS —  PROCESS   DRAWING  — 

PATENT   OFFICE   DRAWING. 

82.  Mechanical  Copying,     (a)     A  tracing-paper  transfer.     Place,  tracing  paper 
over  the  outline  required  to  be  copied.     Trace  the  outline;  turn  the  paper  over; 
go  over  the  traced  line  with  a  soft  pencil,  and  rub  down  the  lead.     Reverse  the 
tracing  paper,  place  it  on  the  drawing  and  go  over  the  traced  line  with  a  3H  pencil. 
Instead  of  rubbing  lead  on  the  back  of  the  traced  line,  a  transfer  paper  —  pre- 
pared by  rubbing  powdered  lead  uniformly  on  tissue  paper  —  may  be  placed  be- 
tween the  tracing  and  the  drawing  paper. 

(£)  A  celluloid  transfer.  A  sharper  and  narrower  line  than  by  the  preceding 
methods  may  be  obtained  by  making  the  tracing  on  thin  celluloid,  with  a  sharp  steel 
point.  Go  over  the  back  of  the  traced  line  with  a  steel  point,  and  then  rub  into 
the  line  the  lead  of  a  black  or  a  blue  pencil.  Dust  off  the  superfluous  lead,  place 
the  celluloid  with  the  lead-filled  line  next  to  the  paper,  and  then  rub  the  line 
briskly  with  the  burnisher. 

(c)  A  rubbing.  The  outlines  of  forms  in  relief,  such  as  ornament  and  letter- 
ing, may  be  obtained,  if  their  edges  are  fairly  sharp,  by  placing  thin  paper  over  the 
forms,  and  then  rubbing  over  their  edges. 

83.  Enlargement  and  Reduction,     (a)     By  pantograph.     Irregular    figures, 
such  as  maps  and  diagrams,  may  be  enlarged  or  reduced  with  a  fair  degree  of  accu- 
racy by  means  of  an  inexpensive  pantograph.    An  expensive  form  of  this  instrument 
is  necessary  for  accurate  engineering  work. 

(b]  By  triangulation,  base  lines,  and  offsets.  First  establish  the  principal 
points  of  the  given  outline  by  a  series  of  triangles,  built  up  from  a  base  line  connect- 
ing any  two  important  points  in  the  given  outline,  and  then  tie  in  additional  points 
by  means  of  offsets  from  the  sides  of  the  triangles  taken  as  additional  base  lines. 
Begin  the  enlargement  or  reduction  by  drawing  a  line  proportional  to  the  prin- 
cipal base  line  in  the  original,  and,  starting  from  this  base  line,  draw  triangles  and 
offsets  proportional  to  those  on  the  original.  Having  thus  determined  the  position 
of  the  principal  points,  the  outline  must  be  sketched  in  by  eye.  The  proportional 
distances  used  in  constructing  the  triangles  may  be  obtained  by  the  use  of  two 
scales,  or  with  the  proportional  dividers.  If  the  size  of  the  original  and  of  the 

(183) 


1 84 


ENLARGEMENT  AND  REDUCTION. 


reduction  or  enlargement  will  permit,  place  the  paper  on  which  the  copy  is  to  be 
made  close  to  the  original,  and  obtain  the  triangles  for  the  copy  by  means  of  lines 
—  drawn  by  sliding'the  triangle  (Art.  23) —  parallel  to  the  sides  of  the  triangles  in 
the  original. 


Fig.  157. 

(c)     By  proportional  squares.     Let  it  be  supposed  that  it  is  required  to  make 
from  a  photograph  or  a  cut,  Fig.  157,  a  large  wall  diagram  to  illustrate  this  machine. 


Fig.  158. 

Circumscribe  a  rectangle  about  the  photograph,  and  rule  lines,  as  i,  2, —  43,  Fig. 
158,  dividing  the  rectangle  into  squares.  Begin  the  diagram,  Fig.  159,  by  drawing 
a  rectangle  of  the  size  required,  and  having  the  sides  proportional  to  those  of  the 


ENLARGEMENT  AND  REDUCTION. 


rectangle,  Fig.  158.  Divide  the  sides  i  —  25  and  25 — 43,  Fig.  159,  into  the 
number  of  parts  used  on  the  original,  Fig.  158,  and  draw  the  horizontal  and  vertical 
lines  as  shown.  Find  the  vanishing  points  VPZ  and  VP3  (the  latter  is  at  the  inter- 
section of  the  lines  A,  B, — L,  Fig.  159;  also  see  note  on  the  cut  of  the  original, 
Fig.  158)  by  producing  several  of  the  convergent  lines,  and  draw  the  horizon. 


i»     ''    /«.  a    it-    if  '*    »/ 


/    i    *    +    If  I    7    r 


Fig.  159. 


Draw  the  horizon,  Fig.  159,  and  locate  the  vanishing  points  by  laying  off  on  the 
horizon  the  necessary  (proportional)  distances.  Note  the  point  where  a  line  crosses 
the  edge  of  a  square  in  the  original,  Fig.  158,  and  sketch  the  line  through  the  cor- 
responding point  (judged  by  eye)  in  the  corresponding  square  on  the  diagram,  Fig. 
159.  The  convergent  lines  should  be  ruled  with  the  aid  of  a  long  straight-edge 
passed  through  the  proper  vanishing  point. 

If  there  is  objection  to  drawing  directly  lines  on  an  original,  the  squares  may 
be  drawn  on  tracing  paper  placed  over  the  original. 

In  making  a  copy  directly  from  a  flat  (actual)  object,  it  is  sometimes  con- 
venient, first,  to  obtain  its  outline  by  running  a  pencil  around  the  object  laid  on 
paper,  after  which  the  outline  may  be  enlarged  or  reduced  by  any  of  the  methods 
described. 


1 86  THE  BLUE-PRINT  PROCESS. 

84.  The  Blue-print  Process.  Blue-print  paper  is  a  white  paper  with  a  coating 
which  is  sensitive  to  light.  So  long  as  the  paper  is  protected  from  light,  the  coat- 
ing can  be  easily  removed  by  washing ;  but  on  exposure  to  sunlight  the  coating 
turns  blue,  and  becomes  insoluble  in  water. 

A  print  is  obtained  by  means  of  a  wooden  frame  set  with  glass,  and  having  a 
removable  back  lined  with  felt.  The  drawing,  preferably  a  tracing,  is  placed  with 
the  ink  lines  next  to  the  glass  ;  the  blue-print  paper  with  the  sensitized  surface  next 
to  the  tracing.  The  frame  is  then  exposed  to  direct  sunlight,  which,  passing  through 
the  portion  of  the  tracing  cloth  not  covered  by  the  ink  lines,  acts  on  the  sensitized 
surface,  while  the  portions  of  this  surface  protected  by  the  lines  of  the  tracing  are 
not  affected.  After  an  exposure  varying  from  twenty  seconds  to  five  minutes,  de- 
pendent upon  the  "speed"  of  the  paper,  the  print  is  thoroughly  washed  in  a  tank 
of  running  water  or  by  means  of  a  hose.  The  print  is  then  hung  up,  that  it  may 
drain  properly  and  dry  flat.  A  good  print  shows  clear  white  lines  on  a  uniform 
blue  ground. 

When  the  back  of  the  printing  frame  is  in  position,  the  blue-print  paper,  the 
tracing,  and  the  glass  should  be  in  close  contact.  If  the  contact  is  imperfect,  it 
should  be  corrected  by  means  of  a  felt  pad ;  otherwise  more  or  less  light  will  pass 
under  the  lines,  with  the  result  that  edges  of  the  white  lines  in  the  print  will  be 
blurred,  or  the  lines  tinged  with  blue. 

If  a  print  is  under-exposed,  it  washes  out  to  a  pale  greenish  blue,  giving  a 
weak  contrast  with  the  white  lines.  If  a  print  is  over-exposed,  the  light  is  likely  to 
work  through  the  lines  of  the  tracing,  in  which  case  the  lines  on  the  print  wash  out 
to  a  pale  blue  instead  of  white,  and  the  ground  becomes  too  dark  or  turns  gray. 

Special  care  must  be  taken  to  exclude  all  light  from  quick  papers  —  a  covered 
case  or  can  is  convenient  —  and  to  open  them  only  in  a  subdued  light  or  a  dark 
room.  Quick  papers  may  be  printed  by  electric  light. 

As  excellent  prepared  blue-print  papers,  of  different  speeds,  can  be  purchased 
at  a  moderate  price,  it  is  usually  not  worth  while  for  the  draftsman  to  coat  his  own 
paper.  The  process,  however,  is  as  follows  :  — 

For  a  paper  requiring  an  exposure  of  about  five  minutes,  mix  separately, 

(1)  Red  Prussiate  of  Potash  (recrystalized)  i  part  (by  weight) 
Water                                                                   5  parts   "         " 

(2)  Citrate  of  Iron  and  Ammonia  i  part     "         " 
Water                                                                   5  parts   "         " 

Working  in  a  subdued  light,  mix  equal  parts  of  these  solutions,  and  apply  to 
the  paper  with  a  sponge,  or  a  flat  3-inch  camel-hair  brush.  (For  a  quicker  paper 
more  of  the  citrate  of  iron  solution  must  be  used,  but  the  color  of  the  print  will  not 
be  so  good.)  A  good  quality,  hard  surface  paper  should  be  used.  As  the  solutions 
/  and  2  are  not  affected  by  light,  they  may  be  kept  on  hand  ready  for  use. 


THE   BLUE-PRINT  PROCESS  —  PROCESS  DRAWING.  187 

Blue  lines  on  a  ivhite  ground  (positive  prints) .  Make  a  preliminary  negative 
on  thin  brown-print  paper  —  obtained  of  dealers  in  drawing  supplies  —  with  the 
tracing  reversed  ;  that  is,  with  the  ink  lines  next  to  the  sensitized  surface.  Substi- 
tute the  brown-print  negative,  which  shows  white  lines  on  a  brown  ground,  for  the 
tracing,  and  proceed  as  described  for  the  prints  on  a  blue  ground. 

Good  blue  prints  can  be  made  from  drawings  on  thin,  or  on  bond  paper.  When 
a  blue  print  is  to  be  made  from  a  drawing  on  thick  paper,  the  drawing  may  be  made 
more  transparent  by  wetting  with  naphtha  or  gasolene,  which  dries  out  without 
injury  to  the  drawing.  For  a  sharp  print  it  is  necessary,  in  order  to  exclude  the 
oblique  rays  which  will  pass  under  the  lines,  to  lay  the  drawing  face  down,  but 
with  the  disadvantage  that  the  print  is  reversed. 

When  a  part  of  a  drawing  is  not  wanted  in  a  print,  the  part  may  be  covered 
with  thick  paper  placed  between  the  tracing  and  the  glass  of  the  printing  frame. 
Pencil  lines  and  spots  may  be  removed  from  a  tracing  by  sponging  with  naphtha  or 
gasolene,  which  does  not  injure  the  cloth  or  the  ink  lines. 

For  making  alterations  on  a  blue  print,  white  lines  may  be  made  with  soda, 
or  any  alkali,  dissolved  in  water,  with  a  small  quantity  of  gum  arabic  added  to  pre- 
vent the  mixture  from  spreading  on  the  blue  print ;  or  black  drawing  ink  may  be 
used  on  light  blue  prints,  and  red  ink  on  dark  ones. 

Blue  prints  required  to  stand  much  handling,  if  the  size  permits,  may  be 
mounted  on  binder's  board  and  then  shellacked. 

85.  Process  Drawing.     A  drawing  made  to  be  reproduced  by  any  of  the  photo- 
mechanical processes,  such  as  photo-engraving  and  photo-lithography,  is  termed  a 
process  drawing. 

The  practical  bearing  of  the  special  requirements  in  this  kind  of  drawing  will 
be  better  understood  from  a  brief  description  of  the  processes  of  photo-engraving. 

86.  Line  Plates.     A  line  plate  is  one  which  reproduces  an  outline  drawing. 
The  photographic  negative.     A    negative   of   the  drawing  is  made   by  means 

of  a  wet  plate,  so  prepared  that  the  film  or  negative  can  be  pulled  ("stripped") 
from  the  glass.  After  exposure  in  the  camera,  the  negative  is  developed,  sub- 
jected to  various  chemical  processes,  and  then  stripped. 

The  zinc  transfer.  When  dry,  the  film  is  reversed,  placed  on  a  thick  plate 
of  glass,  and  a  print  is  made  on  a  sheet  of  highly  polished  zinc  or  copper,  coated 
with  a  mixture  of  glue  sensitized  with  bichromate  of  ammonia.  The  mounted 
film  and  the  sheet  of  metal  are  placed  in  a  heavy  printing  frame,  and  exposed  to 
light,  as  in  blue  printing ;  the  light  causes  the  sensitized  glue  to  become  insoluble 
in  water.  The  print  is  washed,  to  remove  the  portions  of  the  coating  not  affected 
by  the  light,  and  then  "  burned  in  "  by  exposure  to  an  intense  heat,  which  car- 
bonizes the  insoluble  glue  remaining  on  the  plate. 


1 88  PROCESS  DRAWING  —  LINE  PLATES. 

Etching.  The  plate  is  placed  in  a  solution  of  nitric  acid,  which  eats  out 
the  surface  not  covered  by  the  carbonized  glue.  After  a  short  exposure  to  the 
acid  ("  first  bite ")  the  plate  is  dried  and  brushed  over  with  powdered  dragons- 
blood,  to  protect  the  sides  of  the  lines  from  the  acid,  which  would  otherwise  attack 
the  lines  beneath  the  carbonized  surface,  and  thus  produce  what  is  technically  called 
"  undercutting."  The  etching  and  the  application  of  the  dragons-blood  are  done 
three  times  (four  times  for  extra  deep  etching). 

Finishing.  The  plate  now  goes  to  the  engraver,  to  be  cleaned  up  by 
hand  ;  after  which  the  relief  of  the  lines  is  increased  by  cutting  the  ground  of  the 
plate  deeper  with  the  "routing1"  machine.  The  plate  is  then  proved  on  a  printing 
press ;  finally  it  is  nailed  to  a  block  to  bring  it  to  the  height  .of  printer's  type. 

87.  Drawings  for  Line  Plates.  The  first  step  toward  securing  excellence  in 
a  line  plate  is  attention  to  details  in  making  the  original  drawing. 

To  obtain  a  greater  sharpness  of  line  when  the  drawing  is  photographed,  also 
to  eliminate  imperfections  as  far  as  possible,  the  drawing  should  be  made  larger  than 
the  plate.  Over-reduction,  however,  may  result  in  broken  or  ragged  lines  in  the 
plate,  a  weak-looking  cut,  or  one  so  small  that  its  details  may  not  easily  be  seen. 
The  best  results  are  obtained  from  a  drawing  made  from  one-third  to  one-half  larger 
than  the  plate.  Make  the  drawing  on  smooth,  white  bristol  board,*  and  keep  it 
clean.  See  that  all  lines  of  the  drawing  have  sharp,  smooth  edges,  and  that  the 
lines  are  black.  If  the  plate  is  to  be  considerably  smaller  than  the  drawing,  ample 
allowance  must  be  made  for  the  reduction  in  line  widths,  in  order  that  the  lines  on 
the  plate  may  not  come  so  fine  that,  unless  retouched  on  the  zinc  —  not  always 
skilfully  done  —  there  will  be  danger  of  the  lines  breaking  down  from  undercutting. 
In  "  forcing  "  the  line  widths  in  a  drawing,  as  necessary  for  a  considerable  reduc- 
tion, the  beginner  must  not  be  misled  by  the  difference  between  the  appearance  of 
his  process  drawing  and  that  of  an  engineering  drawing,  since,  as  compared  with 
the  latter,  the  former  may  appear  altogether  too  heavy.  In  dimensioning  and  letter- 
ing a  drawing,  it  is  specially  important  to  allow  for  the  reduction,  as  a  reduction 
satisfactory  for  the  drawing  may  bring  the  letters  to  a  size  not  easily  read.  A 
reducing  glass  will  give  some  idea  of  the  appearance  of  a  reduction,  the  approximate 
size  of  which  may  be  obtained  by  measuring  the  image  on  the  glass. 

When  very  narrow  lines  on  the  plate  are  desired,  it  should  be  remembered 
that  ragged  lines  tend  to  thicken  in  the  photographic  negative.  A  perfectly  smooth 
line  on  the  drawing  will  give  a  narrower  line  on  the  plate  than  will  a  ragged  line 
of  the  same  or  even  less  width. 

A  rubber  must  be  used  with  caution  on  a  process  drawing,  as  its  use  will 
quickly  make  black  lines  gray. 

*  Drawings  on  tracing  cloth  give  excellent  results,  but  correction  is  more  difficult. 


PROCESS  DRAWING — HALF-TONE  PLATES.  189 

Special  methods.  White  lines  —  ruled  or  freehand  —  on  a  black  ground 
may  be  obtained  by  laying  in  the  ground  and  then  drawing  the  lines  in  Chinese 
white.  The  white  (Plate  3)  must  be  diluted  with  water,  and  the  proper  thickness 
must  be  judged  from  trial  lines,  which  must  be  allowed  to  dry,  as  the  dry  pigment 
is  whiter  than  the  liquid.  The  black  ground  must  be  laid  in  with  waterproof  ink. 

Dash  lines  may  be  ruled  solid  in  waterproof  ink,  and  the  dashes  may  be 
obtained  by  cutting  the  line  with  the  white,  applied  with  a  brush. 

Methods  of  correction.  Minor  corrections  can  be  made  to  advantage  with 
Chinese  white.  For  example,  the  width  of  a  line  may  be  reduced  and  ragged  edges 
removed  by  ruling  a  line  with  the  white,  applied  with  the  ruling  pen.  Letters  may 
be  cleaned  up  and  their  outlines  corrected  by  means  of  the  white,  applied  with 
a  small,  sharp-pointed  brush.  It  is  necessary,  however,  to  use  the  white  with  cau- 
tion ;  as  the  pigment  accumulates  rapidly,  several  applications  of  it  may  be  suf- 
ficient to  cast  a  shadow  when  the  drawing  is  photographed.  If  a  correction  is  not 
satisfactory,  scrape  off  the  white  and  correct  again.  As  a  slight  film  of  the  white 
over  black  will  prevent  the  black  from  photographing,  it  is  a  good  plan  to  look  over 
all  Chinese  white  corrections  with  a  magnifying  glass  before  sending  the  drawing 
away.  Lines  should  never  be  cleaned  up  with  a  steel  eraser,  as  furred  edges  in  the 
drawing  are  exaggerated  by  the  camera. 

When  necessary  to  redraw  a  line,  it  is  better  to  draw  the  line  on  thin,  smooth 
paper  pasted  over  the  line  than  on  a  surface  furred  up  by  erasure.  The  edges  of 
a  patch  however,  cast  a  shadow  which  must  be  removed  by  the  engraver ;  hence 
the  edges  of  the  patch  must  be  kept  as  far  away  as  possible  from  lines  of  the 
drawing,  in  order  that  the  engraver  may  have  sufficient  space  in  which  to  work. 

If  any  considerable  portion  of  a  drawing  must  be  corrected,  the  place  may  be 
patched  as  just  described,  or  the  place  may  be  cut  out  and  fresh  piece  of  card- 
board inserted.  If  the  latter  method  is  adopted,  the  inserted  cardboard  must 
match  that  on  which  the  drawing  is  made,  since  a  difference  in  the  shade  and 
cleanliness  of  the  two  pieces  may  show  in  the  negative,  and  thereby  affect  the 
quality  of  the  line  plate. 

88.  Half-tone  Plates.  The  reproduction,  by  a  plate,  of  light  and  shade 
drawings  must  be  done  by  the  half-tone  process,  which  is  similar  to  that  of  the  line 
plate  with  the  following  exceptions :  The  drawing  is  photographed  through  a 
screen  —  composed  of  lines  ruled  on  glass  —  placed  close  to  the  sensitized  plate. 
The  image  of  the  screen  appears  on  the  negative,  breaking  up  the  image  of  the 
drawing  into  minute  points  of  varying  character;  and  the  duplication  of  these 
points  on  copper  constitutes  the  half-tone  plate.  The  etching  of  the  plate  —  done 
with  perchloride  of  iron  instead  of  with  nitric  acid  —  takes  considerably  more  time 
than  the  etching  of  a  line  plate. 


190    DRAWINGS  FOR  HALF-TONE  PLATES  —  PATENT  OFFICE  DRAWING. 

The  coarseness  of  the  screen  is  measured  by  the  number  of  its  lines  to  an 
inch,  and  the  particular  screen  used  depends  upon  the  character  of  the  printing  in 
which  the  plate  will  be  used.  For  the  coarsest  newspaper  work  a  screen  of  65 
lines  is  used,  and  for  fine  book  work  a  screen  of  200  lines,  although  as  high  as 
400  lines  has  been  used.  (The  screen  for  Plate  22  was  one  of  175  lines.)  The 
finer  finish  of  half-tone  plates  is  the  work  of  skilled  (hand)  engravers,  and  finishers 
who  re-etch  locally  with  a  brush.  A  plate  is  darkened  by  burnishing  and  lightened 
by  re- etching. 

89.  Drawings  for  Half-tone  Plates.  Black  and  white  drawings  for  half-tone 
plates  are  made  in  the  usual  manner.  Lamp  black  is  perhaps  the  best  medium  to 
use,  although  good  results  attend  the  use  of  India  ink,  charcoal  gray,  etc.  Unless 
it  is  desired  to  have  the  grain  of  the  paper  show  in  a  print,  very  smooth  paper  must 
be  used.  The  whitest  of  paper  is  reproduced  by  a  tint  in  the  plate  (see  Fig.  G, 
Plate  19,  showing  the  tint  of  the  paper  on  which  the  hook  was  drawn)  ;  hence,  for 
a  reproduction  on  a  white  ground,  the  tint  must  be  removed  by  the  engraver  and 
the  routing  machine  (see  Plate  22).  When  the  tint  is  to  be  removed,  the  engraver 
will  be  materially  assisted,  in  mechanical  subjects,  if  the  boundary  of  the  drawing 
is  defined  by  a  line  in  Chinese  white. 


Fig.  1 60. 

90.  Patent  Office  Drawing.  An  application  for  a  patent  must  be  accom- 
panied by  a  drawing  made  in  accordance  with  the  requirements  contained  in  the 
extract  from  the  "  Rules  of  Practice  of  the  United  States  Patent  Office "  which 
follows.  Any  system  of  drawing,  such  as  orthographic  projection,  perspective,  iso- 


PATENT  OFFICE  DRAWING.  191 

metric,  etc.,  may  be  used,  and  the  one  selected  should  be  that  which  will  show  the 
invention  to  the  best  advantage. 

The  cuts,  Figs.  A  and  B,  Plate  23,  reproduced  from  the  "Rules  of  Practice," 
indicate  the  character  of  patent-office  drawings.  It  will  be  seen  that  the  upper 
left-hand  view,  Fig.  B,  is  in  isometric,  while  the  other  views  are  orthographic  pro- 
jections. In  the  case  of  a  drawing  such  as  is  shown  in  Fig.  A,  considerable  line 
shading  is  permissible,  but  it  should  be  used  sparingly  in  drawings  of  machinery. 
For  example,  the  drawing,  Fig.  160,  is  overshaded ;  other  objections  to  this  draw- 
ing are  the  placing  of  letters,  as  N,  K,  and  Q,  on  shaded  surfaces  and  the  unneces- 
sary representations  of  wood  and  stone. 

A  plate  giving  the  conventions  to  be  used  in  drawings  of  electrical  apparatus 
will  be  found  opposite  page  86  of  the  "  Rules  of  Practice." 

Extract  from  the  "Rules  of  Practice  of  the  United  States  Patent  Office"  : 

"...  The  applicant  for  a  patent  is  required  by  law  to  furnish  a  drawing  of  his 
invention  whenever  the  nature  of  the  case  admits  of  it. 

.  .  .  The  drawing  may  be  signed  by  the  inventor,  or  the  name  of  the  inventor 
may  be  signed  on  the  drawing  by  his  attorney  in  fact,  and  must  be  attested  by  two 
witnesses.  The  drawing  must  show  every  feature  of  the  invention  covered  by  the 
claims,  and  the  figures  should  be  consecutively  numbered  if  possible.  When  the 
invention  consists  of  an  improvement  on  an  old  machine  the  drawing  must  exhibit, 
in  one  or  more  views,  the  invention  itself,  disconnected  from  the  old  structure,  and 
also  in  another  view  so  much  only  of  the  old  structure  as  will  suffice  to  show  the 
connection  of  the  invention  therewith. 

.  .  .  Three  several  editions  of  patent  drawings  are  printed  and  published, — 
one  for  office  use,  certified  copies,  etc.,  of-  the  size  and  character  of  those  attached 
to  patents,  the  work  being  about  6  by  Q|-  inches ;  one  reduced  to  half  that  scale, 
or  one-fourth  the  surface,  of  which  four  are  printed  on  a  page  to  illustrate  the 
volumes  distributed  to  the  courts  ;  and  one  reduction  —  to  about  the  same  scale  — 
of  a  selected  portion  of  each  drawing  for  the  Official  Gazette. 

This  work   is  done  by  the  photolithographic  process,  and  therefore  the  char- 
acter of  each  original  drawing  must  be  brought  as  nearly  as  possible  to  a  uniform 
standard  of  excellence,  suited  to  the  requirements  of  the  process,  and  calculated  to 
give  the  best  results,  in  the  interests  of  inventors,  of  the  office,  and  of  the  public. 
The  following  rules  will  therefore  be  rigidly  enforced,  and  any  departure  from  them 
will  be  certain  to  cause  delay  in  the  examination  of  an  application  for  letters  patent : 
(i)     Drawings  must  be  made  upon  pure  white  paper  of  a  thickness  cor- 
responding to  three-sheet   Bristol  board.     The  surface  of  the  paper  must  be 
calendered  and  smooth.     India  ink  alone  must  be  used,  to  secure  perfectly 
black  and  solid  lines. 


192  PATENT  OFFICE  DRAWING. 

(2)  The  size  of  a  sheet  on  which  a  drawing  is  made  must  be  exactly  10 
by  15  inches.     One  inch  from  its  edges  a  single  marginal  line  is  to  be  drawn, 
leaving  the  "sight"  precisely  8  by  13  inches.     Within  this  margin  all  work 
and  signatures  must  be  included.     One  of  the  shorter  sides  of  the  sheet  is 
regarded   as  its   top,  and,  measuring  downwardly  from  the  marginal  line,  a 
space  of  not  less  than  i^  inches  is  to  be  left  blank  for  the  heading  of  title, 
name,  number,  and  date. 

(3)  All   drawings  must  be  made  with  the  pen  only.     Every  line  and 
letter  (signatures  included)  must  be  absolutely  black.     This  direction  applies 
to  all  lines,  however  fine,  to  shading,  and  to  lines  representing  cut  surfaces  in 
sectional  views.     All  lines  must  be  clean,  sharp,  and  solid,  and  they  must  not 
be  too  fine  or  crowded.     Surface  shading,  when  used,  should  be  open.     Sec- 
tional shading  should  be  made  by  oblique  parallel  lines,  which  may  be  about 
one-twentieth  of  an  inch  apart.     Solid  black  should  not  be  used  for  sectional 
or  surface  shading. 

(4)  Drawings  should  be  made  with  the  fewest  lines  possible  consistent 
with  clearness.     By  the  observance  of  this  rule  the  effectiveness  of  the  work 
after  reduction  will  be  much  increased.     Shading  (except  on  sectional  views) 
should  be  used  only  on  convex  and  concave  surfaces,  where  it  should  be  used 
sparingly,  and  may  even  there  be  dispensed  with  if  the  drawing  is  otherwise 
well  executed.     The  plane  upon  which  a  sectional  view  is  taken  should  be 
indicated  on  the  general  view  by  a  broken  or  dotted  line.     Heavy  lines  on  the 
shade  sides  of  objects  should  be  used,  except  where  they  tend  to  thicken  the 
work  and  obscure  letters  of  reference.     The  light  is  always  supposed  to  come 
from  the  upper  left-hand  corner  at  an  angle  of  forty-five  degrees.     Imitations 
of  wood  or  surface  graining  should  not  be  attempted. 

(5)  The  scale  to  which  a  drawing  is  made  ought  to  be  large  enough  to 
show  the  mechanism  without  crowding,  and  two  or  more  sheets  should   be 
used  if   one  does  not  give  sufficient  room  to  accomplish  this  end ;  but  the 
number  of  sheets  must  never  be  more  than  is  absolutely  necessary. 

(6)  The  different  views    should  be   consecutively  numbered.     Letters 
and  figures  of  reference  must  be  carefully  formed.     They  should,  if  possible, 
measure  at  least  one-eighth  of  an  inch  in  height,  so  that  they  may  bear  re^luc- 
tion  to  one  twenty-fourth  of  an  inch ;  and  they  may  be  much  larger  when 
there  is  sufficient  room.     They  must  be  so  placed  in  the  close  and  complex 
parts  of  drawings  as  not  to  interfere  with  a  thorough  comprehension  of  the 
same,  and   therefore  should  rarely  cross  or  mingle  with  the  lines.     When 
necessarily  grouped  around  a  certain  part,  they  should  be  placed  at  a  little 
distance,  where  there  is  available  space,  and  connected  by  short  broken  lines 


ffi 

bJD 
LL 


(i93) 


PATENT  OFFICE  DRAWING.  195 

with  the  parts  to  which  they  refer.  They  must  never  appear  upon  shaded 
surfaces,  and,  when  it  is  difficult  to  avoid  this,  a  blank  space  must  be  left  in 
the  shading  where  the  letter  occurs,  so  that  it  shall  appear  perfectly  distinct 
and  separate  from  the  work.  If  the  same  part  of  an  invention  appear  in  more 
than  one  view  of  the  drawing,  it  must  always  be  represented  by  the  same 
character,  and  the  same  character  must  never  be  used  to  designate  different 
parts. 

(7)  The  signature  of  the  inventor  should  be  placed  at  the  lower  right- 
hand  corner  of  each  sheet,  and  the  signatures  of  the  witnesses  at  the  lower 
left-hand  corner,  all  within  the  marginal  line,  but  in  no  instance  should  they 
trespass  upon  the  drawings.     (See  specimen  drawing.  .  .  .)     The  title  should 
be  written  with  pencil  on  the  back  of  the  sheet.     The  permanent  names  and 
title  will  be  supplied  subsequently  by  the  office  in  uniform  style. 

When  views  are  longer  than  the  width  of  the  sheet,  the  sheet  should  be 
turned  on  its  side  and  the  heading  will  be  placed  at  the  right  and  the  sig- 
natures at  the  left,  occupying  the  same  space  and  position  as  in  the  upright 
views,  and  being  horizontal  when  the  sheet  is  held  in  an  upright  position ;  and 
all  views  on  the  same  sheet  must  stand  in  the  same  direction.  One  figure 
must  not  be  placed  upon  another  or  within  the  outline  of  another. 

(8)  As  a  rule,  one  view  only  of  each  invention  can  be  shown  in  the 
Gazette  illustrations.     The  selection  of  that  portion  of  a  drawing  best  calcu- 
lated to  explain  the  nature  of  the  specific  improvement  would  be  facilitated 
and  the  final  result   improved   by  the  judicious  execution  of  a  figure  with 
express  reference  to  the  Gazette,  but  which  might  at  the  same  time  serve  as 
one  of  the  figures  referred  to  in  the  specification.     For  this  purpose  the  figure 
may  be  a  plan,  elevation,  section,  or  perspective  view,  according  to  the  judg- 
ment of   the  draftsman.     It  must   not  cover  a  space   exceeding   16  square 
inches.     All  its  parts  should  be  especially  open  and  distinct,  with  very  little 
or  no  shading,  and  it  must  illustrate  the  invention  claimed  only,  to  the  exclu- 
sion of  all  other  details.     (See  specimen  drawing.)     When  well  executed,  it 
will  be  used  without  curtailment  or  change,  but  any  excessive  fineness,  or 
crowding,  or  unnecessary  elaborateness  of  detail  will  necessitate  its  exclusion 
from  the  Gazette. 

(9)  Drawings    should   be   rolled   for    transmission    to    the   office,   not 
folded." 


DECIMAL  EQUIVALENTS   OF  FRACTIONS  OF  AN   INCH. 


*V  -0156 

&   -*4o6 

H   -2656 

M  .3906 

If  -  -5'  56 

n  -6406 

II   -7656 

Ji  -8906 

A  -0313 

A   -'563 

A   -28l3 

if   -4063 

il  -5313 

n  -6563 

1!  -7813 

M  -9063 

s3?   -0469 

U   -'719 

H  -2969 

H  -4*19 

M  -5469 

1!  -6719 

M  -7969 

if  -9219 

A   -°625 

A  -1875 

A   -3  I25 

T7*   -4375 

A  -5625 

tt  -6875 

it  -8125 

H  -9375 

ft   .0781 

if  -2031 

*1   -3281 

II   -453' 

Si  -5781 

II  -7031 

H  -8281 

tt  -9531 

A    -0938 

A  -2l88 

H  -3438 

M   -4688 

if  -5938 

II  .7188 

i£  .8438 

n  -9688 

&    -1094 

il  -2344 

II   -3594 

H   .4844 

II  -6094 

1}   -7344 

H  -8594 

II  .9844 

i   .1250 

j  .2500 

1   -375° 

|   .5000 

§•   .6250 

*   .7500 

*   .8750 

I  1  .0000 

INCHES   AND   FRACTIONS   REDUCED   TO  DECIMALS   OF  A  FOOT. 


Inch 

1" 

2" 

3" 

4" 

5" 

6" 

1" 

8" 

9" 

10" 

11" 

Inch 

.000 

.083 

.167 

•250 

•333 

.417 

.500 

•583 

.667 

.750 

•833 

.917 

A" 

.005 

.089 

.172 

•255 

•339 

.422 

.505 

•589 

.672 

•755 

•839 

.922 

A* 

r 

.010 

.094 

.177 

.260 

•344 

.427 

.510 

•594 

.677 

.760 

.844 

.927 

Y 

Tv 

.016 

.099 

.182 

.266 

•349 

•432 

•516 

•599 

.682 

.766 

.849 

•932 

A" 

r 

.021 

.104 

.188 

.271 

•354 

•438 

•521 

.604 

.688 

•77i 

.854 

•938 

P 

A" 

.026 

.IO9 

•193 

.276 

•359 

•443 

.526 

.609 

•693 

.776 

•859 

•943 

5» 
T£ 

i" 

.031 

•"5 

.198 

.281 

•365 

•448 

•531 

.615 

.698 

.781 

.865 

.948 

r 

A" 

.036 

.120 

.203 

.286 

•37° 

•453 

•536 

.620 

•703 

.786 

.870 

•953 

A* 

V 

.042 

•125 

.208 

.292 

•375 

.458 

.542 

.625 

.708 

.792 

.875 

•958 

V 

A* 

.047 

.130 

.214 

•297 

.380 

.464 

•547 

.630 

.714 

•797 

.880 

.964 

9  H 
TS 

r 

.052 

•»35 

.219 

.302 

•385 

.469 

•552 

•635 

.719 

.802 

.885 

.969 

K 

»• 

•057 

.141 

.224 

•3°7 

•39i 

•474 

•557 

.641 

.724 

.807 

.891 

•974 

Hf 

r 

.063 

.146 

.229 

•3J3 

•396 

•479 

•563 

.646 

•729 

•813 

.896 

•979 

r 

ir 

.068 

.151 

•234 

•318 

.401 

.484 

.568 

.651 

•734 

.818 

.901 

.984 

ir 

r 

•°73 

.156 

.240 

•323 

.406 

.490 

•573 

.656 

.740 

.823 

.906 

.990 

r 

tr 

.078 

.161 

.245 

•328 

.411 

•495 

•578 

.661 

•745 

.828 

.911 

•995 

H* 

(196) 


INDEX. 


Abstract  Arrangement,  104. 

Angles,  of  15°,  30°,  45°,  60°,  75°,  to  obtain,  21,  22. 

To  dimension,  150. 

Applications  of  Isometric  Drawing,  158. 
Architect's  Method  of  Shade  Lines,  121. 
Architect's  Scale,  26. 
Arrangement,  102. 

Abstract,  104. 

Examples  of,  104. 

Forms  of,  104. 

In  Object  Drawing,  no. 

Of  Views  in  Working  Drawings,  146. 

Study  Plates  for,  131,  132. 

Symmetrical,  104. 

To  balance,  104. 

To  design,  103. 
Arrow  Heads,  50. 

Assembling  of  Details,  Study  Plates  for,  131,  132. 
Assembly  Drawings,  143. 
Axes,  Axonometric,  158. 

Isometric,  155. 

Oblique,  161. 
Axonometric,  Axes,  158. 

Co-ordinates,  161. 

Drawing,  158. 

Projection,  155. 

Balancing,  a  Fraction,  50. 

An  Arrangement,  104. 

A  Title  or  Line  of  Letters,  49. 
Beam  Compass,  29. 
Bicycle  Chain  and  Sprockets,  Shade  Lines,  122. 

Study  Plate,  70. 
Blue  Print,  Process,  186. 

To  correct  a,  187. 
Bolt  Heads,  Chamber  of,  117. 

Dimensioning,  147,  150. 
Border  Line,  50. 

Ruled,  to  lay  out,  51. 
Bow  Compass,  4. 

Care  of,  15. 

Use  of,  27. 


Bow  Spacers,  Care  of,  15. 

Use  of,  29. 
Breaks,  40. 

Rendering  of,  40. 
Brushes  for  Wash  Drawing,  166. 

Care  of,  173. 
Built-up  Wash,  170. 

Cabinet  Maker's  Clamp,  no. 

Doubtful  Lines  on,  118. 

Measurements  for,  no. 

Sketches  for,  no. 

Study  Plates  on,  131. 
Cabinet  Projection,  155,  161. 
Cavalier  Projection,  155,  161. 
Celluloid,  Erasing  Shield,  34. 

Template,  25. 

Transfer,  183. 
Center  Lines,  39. 

Use  of  in  Object  Drawing,  113. 
Chain,  Bicycle,  see  Bicycle  Chain  and  Sprockets. 
Chamfer  of  Nuts  and  Bolt  Heads,  117. 
Circle,  to  describe,  27. 
Circles,  Precision  in  Drawing,  39. 

Radii  of,  to  dimension,  150. 

Diameters  of,  to  dimension,  150. 

Approximate  Construction  in  Isometric,  157 
Circular  Holes,  to  measure,  144. 

To  dimension,  151. 
Clearness  in  Dimensioning,  147. 
Cloth,  Tracing,  see  Tracing  Cloth. 
Collective  Rendering,  112. 

Example  of,  127. 
Common  Working  Methods,  52. 
Compass,  4. 

Beam,  29. 

Bow,  see  Bow  Compass. 

Care  of,  15. 

Setting  for  Scale  Measurement,  30. 

Use  of,  27. 
Compass  Leads,  to  Adjust,  18. 

To  Sharpen,  18. 


(197) 


198 


INDEX. 


Composite  View,  to  dimension,  151. 
Construction,  Geometrical,  79. 

Instrumental,  Study  Plates  on,  59. 

Of  Chamfer,  117. 

Of  Isometric  Circles,  157. 

Of  Screw  Threads,  115. 
Constructive  Stage,  52. 
Conventions,  39 

Breaks,  40. 

Cross  Hatching,  40. 

Finished  Surfaces,  153. 

Graining,  40. 

Line,  39. 

Line  Shading,  40,  152. 

Materials,  40. 

On  Working  Drawings,  152. 

Rendering  of,  40. 

Screw  Threads,  116,  153. 

Study  Plate  of,  69. 

Tapped  Holes,  153. 
Convergent  Lines,  Inking  of,  54 
Co-ordinates,  Axonometric,  161. 

Isometric,  157. 
Copying,  Mechanical,  183. 

Preliminary  to  Object  Drawing,  113. 
Correcting,  a  Blue  Print,  187. 

A  Process  Drawing,  189. 

A  Wash  Drawing,  170. 
Cross  Hatching,  40. 

Rendering  of,  40. 
Curve,  French,  24. 

Use  of,  24. 

Curved  Line  Ruling,  24. 
Curved  Solids,  Isometric  of,  157. 

Modeling  by  Washes,  170. 
Curves,  Oblique,  to  measure,  126. 

Duplication  by  Template,  127. 
Cylinders,  Isometric  of,  157. 

Modeling  by  Washes,  170. 

Dash  Lines,  39. 

Abuse  of,  53. 

Rendering  in  Ink,  53. 

Rendering  in  Pencil,  53. 

Decimal  Equivalents,  Fractions  of  an  Inch,  196. 
Decimals  of  a  Foot,  Inches  and  Fractions  Re- 
duced to,  196. 


Designing  an  Arrangement,  103. 

Detail  Drawings,  143. 

Details,  Assembling  of,  Study  Plates  for,  131, 132 

Diameters,  of  Circles,  to  dimension,  150. 

Of  Solids,  to  dimension,  150. 
Dimension  Line,  50. 
Dimensioning,  49. 

A  Composite  View,  151. 

Angles,  150. 

A  Working  Drawing,  147. 

Circular  Holes,  151. 

Clearness  in,  147. 

Diameters  of  Circles,  150 

Radii  of  Circles,  150. 
Dimensions,  49. 

Form  of,  50,  147. 

Necessary,  147. 

Position  of,  147. 

Special  Forms  of,  149. 

Staggering  of,  149. 

System  of  Placing,  147. 
Dividers,  Hair-spring,  29. 

Precision  in  Spacing  with,  38. 

Proportional,  30. 

Setting  for  Scale  Measurement,  30. 

Spacing  with,  29. 
Dotted  Lines,  39. 

Never  Shaded,  122. 
Double-threaded  Screw,  113. 

Construction  of,  115. 
Doubtful  Lines,  118. 
Drawing,  A  Screw  Thread,  114. 

Assembly,  143. 

Axonometric,  158. 

By  Stages,  52. 

Detail,  143. 

For  Half-tone  Plates,  190. 

For  Line  Plates,  188. 

For  Tracing,  112. 

Inked,  Finishing  an,  53. 

Isometric,  see  Isometric  Drawing. 

Object,  see  Object  Drawing. 

Patent  Office,  190. 

Pencil,  Finishing  a,  53, 

Preliminaries  to,  50. 

Process,  187. 


INDEX. 


Drawing,  to  protect,  51. 

To  trim,  51. 

Wash,  see  Wash  Drawing. 

Working,  see  Working  Drawings. 
Drawing  Board,  4. 

Care  of,  15. 

To  Test,  9. 
Drawing  Paper,  15. 

Care  of,  15. 

Selection  of,  15. 

Sizes  of,  16. 

To  stretch,  166. 
Drawn  Letters,  48. 

Rendering  of,  48. 
Duplication,  by  Use  of  Pricker,  19. 

By  Use  of  Template,  127. 

Mechanical  Copying,  183. 

Of  Objects,  Working  Drawings,  143. 

Engineer's  Method  of  Shade  Lines,  121. 
Engineer's  Scale,  26. 
Enlargement,  183. 

By  Pantograph,  183. 

By  Proportional  Squares,  184. 

By  Triangulation,  183. 
Erasing  Shield,  34. 
Erasure,  33. 

Pencil  Line,  33. 

Ink  Line,  33. 

Use  of  Erasing  Shield,  34. 

From  Tracing  Cloth,  35. 
Examples  of  Selection  and  Arrangement,  104. 

Of  Sketching  and  Measuring  an  Object,  no. 
Extension  Lines,  50,  148. 

Finished  Rendering,  in  Ink,  53. 

In  Pencil,  53. 
Finished  Surfaces,  153. 
Finishing  an  Inked  Drawing,  53. 

A  Pencil  Drawing,  53. 
Finishing  Stage,  53. 
Flat  Wash,  167. 

Precautions  to  secure,  169. 
Foot,  Decimals  of,  196. 
Forms,  of  Arrangement,  104. 

Of  Dimensions,  50,  147. 


Fractions,  Balancing,  50. 

Of  an  Inch,  Decimal  Equivalents  of,  196. 

On  Working  Drawings,  154. 
French  Curve,  24. 

Use  of,  24. 

Geometrical  Construction,  59. 
Geometrical  Problems,  79. 

Solution  by  Working  Methods,  55. 
Graining,  40. 

Rendering  of,  40. 

Hair-spring  Dividers,  4. 

Use  of,  29. 
Half-tone  Plates,  189. 

Drawing  for,  190. 
Hand-rail  Stud,  109. 

Designing  the  Layout,  no. 

Doubtful  Lines  on,  119. 

Measurements  of,  no. 

Sketches  of,  no 

Study  Plate  on,  127. 
Hanger,  Study  Plates  on,  132. 
Holes,  Circular,  to  dimension,  151. 

Circular,  to  measure,  144. 

Tapped,  153. 
Horizontal  Line,  to  rule,  19. 

Inch,  Fractions  of,  Decimal  Equivalents,  196. 
Inches  and  Fractions  Reduced  to  Decimals  of 

a  Foot,  196. 
India  Ink,  13. 

Care  of,  15. 

To  prepare  for  Line  Drawing,  31. 

To  prepare  for  Wash  Drawing,  167. 

Use  of,  30. 
Ink,  Drawing,  31. 

Finished  Rendering  in,  53. 

India,  see  India  Ink. 
Inked  Drawing,  Finishing  an,  53. 
Ink  Eraser,  Steel,  13,  34. 
Inking,  by  Stages,  54. 

Of  Convergent  Lines,  54. 
Ink  Lines,  on  Wash  Drawings,  173. 

To  erase,  33. 

Instrumental  Rendering  and  Construction,  Study 
Plates  on,  59. 


2OO 


INDEX. 


Instruments,  Care  of,  15. 

Case  for,  4. 

Set  of,  3. 

Intersections,  Precision  in  Noting,  38. 
Irregular  Objects,  122. 

Methods  of  Measuring,  122. 

Study  Plate  of,  141. 
Isometric,  Axes,  155. 

Co-ordinates,  156. 
Isometric  Drawing,  155. 

Applications  of,  158. 

Approximate  Construction  of  Circles,  157. 

Curved  Solids,  157. 

Non-isometric  Lines,  156. 

Planes,  157. 

Rectangular  Solids,  155. 

Shade  Lines,  158. 

Spheres,  157. 

Study  Plates  on,  162. 

Layout,  for  Object  Drawing,  no. 

For  Selection  and  Arrangement,  102. 

For  Working  Drawings,  145. 
Leads,  Compass,  see  Compass  Leads. 
Lengthening  Bar,  28. 
Lettering,  43. 

Pens,  44. 

To  grind  a  Ruling  Pen  for,  47. 

With  Ruling  Pen,  44,  47. 
Letters,  Drawn,  48. 

For  Working  Drawings,  154. 

Line  of,  to  balance,  49. 

Sizes  of,  45. 

Stroke,  44. 

Styles  of,  45. 
Line,  Border,  50. 

Conventions,  39. 

Conventions  on  Working  Drawings,  152. 

Curved,  to  rule,  24. 

Dash,  39,  53. 

Dimension,  50. 

Extension,  50. 

Horizontal,  to  rule,  20. 

Ink,  to  erase,  33. 

Intersections,  38. 

Of  Letters,  to  balance,  49. 


Line,  of  Sight,  36. 

Parallel,  to  draw,  22. 
-  Pencil,  to  erase,  33. 

Perpendicular,  to  draw,  22. 

Plates,  187. 

Plates,  Drawing  for,  188. 

Shading,  40. 

Vertical,  to  rule,  21. 

Water,  170. 

Widths  for  Working  Drawings,  39,  145. 
Lines,  Convergent,  to  ink,  54. 

Doubtful,  118. 

Ink,  on  Wash  Drawings,  173. 

Non-isometric,  156. 

Shade,  Rendering  of,  55. 

Shade,  see  Shade  Lines. 

Materials,  Care  of,  15. 

Conventions  for,  40. 

For  Wash  Drawing,  166. 

List  of,  i. 

On  Working  Drawings,  152. 
Measurements,  of  an  Object,  109. 

Of  Cabinet  Maker's  Clamp,  no. 

Of  Hand-rail  Stud,  no. 
Measuring,  a  Screw,  114. 

A  Three-pronged  Hook,  125. 

An  Irregular  Object,  122. 

An  Object,  109. 

Circular  Holes,  144. 

Examples  of,  no. 

For  Working  Drawings,  143. 

Oblique  Curves,  126. 

Turned  Handles,  126. 
Measuring  Point,  18. 
Mechanical  Copying,  183. 
Method  of  Shade  Lines,  Architect's,  121. 

Engineer's,  121. 

Methods,  Common  Working,  52. 
Mixed  Rendering,  122. 

Study  Plate  for,  141. 
Modeling  by  Washes,  170. 

Study  Plates  on,  177. 

Necessary  Dimensions,  147. 
Non-isometric  Lines,  156. 


INDEX.  201 

Numerals  for  Working  Drawings,  154.  Plate    2,      7. 

Nuts,  Chamfer  of,  117.  3,    n. 

Dimensioning,  150.  4,    41. 

5»    45- 

Object,  Measuring  for  Working  Drawings,  143.  6,    61. 

Sketching  for  Working  Drawings,  143.  7,    65. 

Object  Drawing,  109.  8,    67. 

Collective  Rendering,  112.  9,    71. 

Copying  as  a  Preliminary  to,  113.  10,     75. 

Doubtful  Lines,  118.  n,  123. 

Selection  and  Arrangement  of  Views,  no.  12,  129. 

Shade  Lines,  119.  13,  133. 

Sketching  and  Measuring  the  Object,  109.  14,  135. 

Study  Plates  on,  127.  15,  137. 

The  Drawing  for  Tracing,  112.  16,  139. 

The  Layout,  no.  17,  159. 

Objects,  Irregular,  see  Irregular  Objects.  18,  163. 

Oblique,  Axes,  161.  19,  171. 

Projection,  155,  161.  20,  175. 

Oblique  Curves,  Measuring,  126.  21,  179. 

22,  181. 

Pantograph,  Use  in  Enlargement  and  Reduc-  23,  193. 

tion,  183.  Plates,  Line,  187. 

Paper,  Drawing,  see  Drawing  Paper.  Line,  Drawing  for,  188. 

To  stretch,  166.  Half-tone,  189. 

Tracing,  16.  Half-tone,  Drawing  for,  190. 

Parallel  Line,  to  draw,  22.  Study,  see  Study  Plate. 

Patent-office  Drawing,  190.  Position  of  Dimensions,  147. 

Penciling,  52.  Precision,  36. 

Pencil  Drawing,  to  finish,  53.  In  Drawing  Circles,  39. 

Pencil  Line,  to  erase,  33.  In  Noting  Line  Intersections,  38. 

Pencil  Point,  Measuring,  18.  In  Scale  Measurement,  38. 

Ruling,  17.  In  Spacing,  38. 

Sketching,  18.  Preliminaries,  to  Drawing,  50. 

Pencils,  13.  To  Object  Drawing,  113. 

Selection  of,  17.  Preparation  of  an  India  Ink  Wash,  167. 

To  sharpen,  17.  Pricker,  10. 

Use  of,  17.  Use  in  Duplication,  19. 

Pencil  Sharpener,  13.  Use  of,  19. 

Pen,  Ruling,  see  Ruling  Pen.  Prints,  Blue,  184. 

Pens,  Lettering,  44.  Problems,  Geometrical,  79. 

Perpendicular  Line,  to  draw,  22.  Solution  by  Working  Methods,  55. 

Pitch  of  Screw  Threads,  113.  Process,  Blue  Print,  186. 

Planes,  Isometric  of,  157.  Process  Drawing,  187. 

Planning  a  Working  Drawing,  145.  To  Correct,  189. 

Plate    i,    5.  Projection,  Axonometric,  155. 


202 


INDEX. 


Projection,  Cabinet,  155,  161. 

Cavalier,  155,  161. 

Isometric,  155. 

Oblique,  155,  161 

Systems  of,  146. 
Projections,  109. 

Treatment  in  Object  Drawing,  112. 
Proportional    Squares,    Enlargement   and    Re- 
duction by,  184. 
Protecting  a  Drawing,  51. 
Protractor,  24. 
Pseudo-pictorial  Representation,  155. 

Radii  of  Circles,  to  dimension,  150. 
Rectangular  Solids,  Isometric  of,  155. 
Reduction,  183. 

By  Pantograph,  183. 

By  Proportional  Squares,  184. 

By  Triangulation,  183. 
Refinements,  in  Observation,  36. 

In  Ruling  Lines,  37. 

In  Scale  Measurement,  37. 
Rendering,  36. 

Collective,  112. 

Finished  in  Ink,  53. 

Finished  in  Pencil,  53. 

Instrumental,  Study  Plates  on,  59. 

Mixed,  122. 

Of  Breaks,  40. 

Of  Conventions,  40. 

Of  Cross  Hatching,  40. 

Of  Drawn  Letters,  48. 

Of  Graining,  40. 

Of  Letters  with  Ruling  Pen,  44. 

Of  Line  Shading,  43. 

Of  Shade  Lines,  55. 

Of  Stroke  Letters,  44. 

Sketch,  for  Object  Drawing,  109. 
Representation,  Pseudo-pictorial,  155. 
Rubbing,  A,  183. 
Ruled  Border  Line,  50. 

To  lay  out,  51. 
Ruling,  Curved  Line,  24. 

Refinements  in,  37. 

Straight  Line,  19. 
Ruling  Pen,  4. 

Care  of,  15,  32. 


Ruling  Pen,  Lettering  with,  44,  47. 

To  grind  for  Lettering,  47. 

To  sharpen,  32. 

Use  of,  31. 
Ruling  Point,  17. 

Scale,  10. 

Architect's,  26. 

Engineer's,  26. 

For  Working  Drawings,  145. 
Scale  Measurement,  Precision  in,  38. 

Refinements  in,  37. 

Setting  Dividers  for,  30. 
Scales,  25. 
Screw  Threads,  113. 

Conventional,  116. 

Drawing  of,  114. 

Measuring  of,  114. 

On  Working  Drawings,  153. 

Sections  of,  114. 
Selection  and  Arrangement,  102. 

Examples  of,  104. 

For  Object  Drawing. 

Study  Plates  on,  107,  no. 
Shade  Lines,  Architect's  Method  of,  121 

Engineer's  Method  of,  121. 

In  Isometric  Drawing,  158. 

On  Working  Drawings,  152. 

Rendering  of,  55,  119. 

Theory  of,  119. 
Shading,  Line,  40. 

On  Working  Drawings,  152. 

Rendering  of  Line,  43. 
Single  threaded  Screw,  113. 

Construction  of,  115. 

Conventional,  116. 
Sketches,  of  Cabinet  Maker's  Clamp,  no. 

Of  Hand-rail  Stud,  no. 
Sketching  Point,  18. 

An  Object,  109. 

And  Measuring,  Examples  of,  no. 

For  Working  Drawings,  143. 
Solids,  Curved  Isometric  of,  157. 

Diameters  of,  to  dimension,  150. 

Modeling  by  Washes,  170. 

Rectangular,  Isometric  of,  155. 
Spacers,  Bow,  29. 


INDEX. 


203 


Spacing,  29. 

Precision  in,  38. 
Speed,  36. 
Spheres,  Isometric  of,  157. 

Modeling  by  Washes,  170. 
Sprockets,    Bicycle,    see    Bicycle    Chain    and 

Sprockets. 

Squares,    Proportional,   Enlargement    and    Re- 
duction by,  184. 

Square-threaded  Screw,  Construction  of,  116. 
Stage,  Constructive,  52. 

Finishing,  53. 
Stages,  Drawing  by,  52. 

Inking  by,  54. 

Staggering  of  Dimensions,  149. 
Stippling,  173. 
Straight-edge,  20. 
Straight  Line,  Especially  Long,  to  rule,  20. 

Horizontal,  to  rule,  19. 

Parallel,  to  draw,  22. 

Perpendicular,  to  draw,  22. 

Ruling,  19. 

Vertical,  to  rule,  21. 
Stretching  Paper,  166. 
Stroke  Letters,  44. 

Rendering  of,  44. 
Study   Plate    i,    59. 

2,  63. 

3,  69. 

4,  70. 

5,  74- 

6,  107. 

7,  108. 

8,  108. 

9,  127. 
10,  131. 
u,  131. 
12,  132. 

J3>  X32- 

14,  141. 

15,  162. 

16,  165. 

i7»  174- 
18,  177. 

iQ.  177- 

20,    177. 


Study  Plate  21,  177. 
22,  178. 

Surfaces,  Finished,  153. 
Symmetrical  Arrangement,  104. 
System  of  Placing  Dimensions,  147. 
Systems  of  Projection,  146. 

Tapped  Holes,  153. 
Taste,  102. 
Template,  25. 

Use  in  Duplication,  127. 
Testing,  55. 
Tests,  for  Drawing  Board,  9. 

For  Triangles,  9. 

For  T-square,  9. 

Threads,  Screw,  see  Screw  Threads. 
Three-pronged  Hook,  Measuring  a,  125 
Thumb  Tacks,  13. 

Allowance  for,  50. 
Title,  to  balance,  49. 
Titles  on  Working  Drawings,  154. 
Tracing  Cloth,  16. 

Erasure  from,  35. 
Tracing,  Drawing  for,  112. 

For  Working  Drawings,  145. 

To  clean,  187. 
Tracing  Paper,  16. 

Transfer,  183. 
Transfer,  Celluloid,  183. 

Tracing  Paper,  183. 
Triangles,  9. 

Care  of,  15. 

Combinations  of,  22. 

To  test,  9. 

Use  of,  20. 

Use  with  T-square,  21. 

Triangulation,  in  Measuring  Irregular  Objects, 
122. 

In  Enlargement  and  Reduction,  183. 
Trimming  a  Drawing,  51. 
T-square,  9. 

Abuse  of,  51. 

Care  of,  15. 

To  test,  9. 

Use  of,  19. 

Use  with  Triangles,  21. 


204 


INDEX. 


Turned  Handles,  Measuring,  126. 
To  draw,  141. 

United  States   Standard   Screw  Thread,  Con 
struction  of,  115. 

Vertical  Line,  to  rule,  21. 

View,  Composite,  to  dimension,  151. 

Views,  Arrangement  in  Working  Drawings,  146. 

Number  for  Working  Drawings,  145. 

Of  Objects,  109. 
V-threaded  Screw,  Construction  of,  115. 

Wash,  166. 

Built  up,  170. 

Flat,  167. 

Graded,  170. 

India  Ink,  to  prepare,  167. 
Wash  Drawing,  166. 

Care  of  the  Brushes,  173. 

Materials  for,  166. 

Stippling,  173. 

Study  Plates  on,  174. 

To  correct,  170. 
Water  Lines,  170. 
Widths  of  Line,  39. 

For  Working  Drawings,  39,  145. 


Working  Drawings,  143. 

Arrangement  of  Views,  146. 

Blue  Prints,  145. 

Conventions  for,  152. 

Dimensioning,  147. 

Finished  Surfaces,  153. 

General  Directions  for  Making,  145. 

Layout  for,  145. 

Letters  and  Numerals,  154. 

Line  Conventions,  152. 

Line  Widths  for,  39,  145. 

Materials,  152. 

Measuring  for,  143. 

Number  of  Views,  145. 

Planning,  145. 

Scale  for,  145. 

Screw  Threads,  153. 

Shade  Lines,  152. 

Shading,  152. 

Sketching  for,  143. 

Tapped  Holes,  153. 

Titles,  154. 

Tracing,  145. 
Working  Methods,  14. 

Common,  52. 

Solution  of  Geometrical  Problems  by,  55. 


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